{"id":3387,"date":"2022-12-12T06:48:09","date_gmt":"2022-12-12T06:48:09","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3387"},"modified":"2023-01-31T06:51:03","modified_gmt":"2023-01-31T06:51:03","slug":"ncert-solutions-class-8-maths-chapter-12-exponents-and-powers-ex-12-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-12-exponents-and-powers-ex-12-1\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 8 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 12 (Exponents and Powers)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 8 Mathematics <strong>Chapter &#8211; 12 Exponents and Powers <\/strong>Exercise 12.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><strong>Chapter 12: Exponents and Powers<\/strong><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-12-exponents-and-powers-ex-12-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 12.2<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 12.1\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Evaluate:<br \/>\n<\/strong><strong>(i) 3<sup>-2<br \/>\n<\/sup>(ii) (-4)<sup>-2<br \/>\n<\/sup>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\left&amp;space;(\\frac{1}{2}&amp;space;\\right&amp;space;)^{-5}}\" alt=\"\\mathbf{\\left (\\frac{1}{2} \\right )^{-5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong><strong>(i) 3<sup>-2<br \/>\n<\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{3^2}&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{1}{3^2} \\right )\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/strong>\u2235 a<sup>-m<\/sup> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{9}\" alt=\"\\frac{1}{9}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) (-4)<sup>-2\u00a0 <\/sup><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\" data-wp-editing=\"1\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{1}{-4^2}&amp;space;\\right&amp;space;)\" alt=\"\\left (\\frac{1}{-4^2} \\right )\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 a<sup>-m<\/sup> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{16}\" alt=\"\\frac{1}{16}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\left&amp;space;(\\frac{1}{2}&amp;space;\\right&amp;space;)^{-5}}\" alt=\"\\mathbf{\\left (\\frac{1}{2} \\right )^{-5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{2}{1}&amp;space;\\right&amp;space;)^5\" alt=\"\\left ( \\frac{2}{1} \\right )^5\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0<\/strong>\u2235 a<sup>-m<\/sup> <strong>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/> <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">=\u00a02<sup>5<br \/>\n<\/sup>= 32<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2.\u00a0 Simplify and express the result in power notation with a positive exponent:<br \/>\n<\/strong><strong>(i)<\/strong> (-4)<sup>4\u00a0<\/sup>\u00f7(-4)<sup>8<\/sup><br \/>\n<strong>(ii)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{2^3}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{1}{2^3} \\right )^2\" align=\"absmiddle\" \/><br \/>\n<strong>(iii)<\/strong> -(3)<sup>4<\/sup>\u00d7<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{5}{3}&amp;space;\\right&amp;space;)^4\" alt=\"\\left (\\frac{5}{3} \\right )^4\" align=\"absmiddle\" \/><br \/>\n<strong>(iv)\u00a0<\/strong>(3<sup>-7<\/sup>\u00f73<sup>-10<\/sup>)\u00d73<sup>-5<\/sup><br \/>\n<strong>(v)\u00a0<\/strong>2<sup>-3<\/sup>\u00d7(-7)<sup>-3<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) (-4)<sup>4\u00a0<\/sup>\u00f7(-4)<sup>8<\/sup>\u00a0 \u00a0 <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= (-4) <sup>5 &#8211; 8\u00a0<\/sup>\u2235 (a)<sup>m <\/sup>\u00f7(a)<sup>n\u00a0<\/sup>= a <sup>m &#8211; n\u00a0<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= (-4)<sup>&#8211;<\/sup><sup>3<\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{-4^3}\" alt=\"\\frac{1}{-4^3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{-64}\" alt=\"\\frac{1}{-64}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{2^3}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{1}{2^3} \\right )^2\" align=\"absmiddle\" \/>\u00a0\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{(2^3)^2}\" alt=\"\\frac{1}{(2^3)^2}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u2235 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{a}{b}&amp;space;\\right&amp;space;)^m&amp;space;=&amp;space;\\frac{a^m}{b^m}\" alt=\"\\left ( \\frac{a}{b} \\right )^m = \\frac{a^m}{b^m}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2^{3\\times&amp;space;2}}\" alt=\"\\frac{1}{2^{3\\times 2}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2235 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?(a^{m})^n&amp;space;=&amp;space;a^{m\\times&amp;space;n}\" alt=\"(a^{m})^n = a^{m\\times n}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2^6}\" alt=\"\\frac{1}{2^6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">(iii)\u00a0<strong>&#8211; (3)<sup>4 <\/sup>\u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\left&amp;space;(&amp;space;\\frac{5}{3}&amp;space;\\right&amp;space;)^4}\" alt=\"\\mathbf{\\left ( \\frac{5}{3} \\right )^4}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= (-3) <sup>4<\/sup> <strong>\u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5^4}{3^4}\" alt=\"\\frac{5^4}{3^4}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong>\u2235 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{a}{b}&amp;space;\\right&amp;space;)^m&amp;space;=&amp;space;\\frac{a^m}{b^m}\" alt=\"\\left ( \\frac{a}{b} \\right )^m = \\frac{a^m}{b^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= (-1)<sup>4 <\/sup>\u00d7 3<sup>4 <\/sup>\u00d7 <strong><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5^4}{3^4}\" alt=\"\\frac{5^4}{3^4}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2235 <\/strong>(ab)<sup>m\u00a0<\/sup>= a<sup>m<\/sup>b<sup>m<\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\">= 1<sup>\u00a0<\/sup>\u00d7 3<sup>(4 &#8211; 4) <\/sup>\u00d7 5<sup>4<\/sup> \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 3<sup>(4-4)<\/sup>\u00d75<sup>4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/sup>\u2235 (a)m \u00f7(a)n = a<sup>m &#8211; n\u00a0 <\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 3<sup>0<\/sup>\u00d75<sup>4<\/sup>\u00a0= 5<sup>4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/sup>\u2235 a<sup>0<\/sup> = 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv)\u00a0(3<sup>-7<\/sup>\u00f73<sup>-10<\/sup>)\u00d73<sup>-5 <\/sup><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 3 <sup>-7 \u2013 (-10)\u00a0<\/sup>\u00d7 3<sup>-5\u00a0 \u00a0\u00a0<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 (a)m \u00f7(a)n = a<sup>m &#8211; n<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 3<sup>(-7+10)<\/sup>\u00d73<sup>-5<br \/>\n<\/sup>= 3<sup>3<\/sup>\u00d73<sup>-5<br \/>\n<\/sup>= 3<sup>(3-5)<br \/>\n<\/sup>= 3<sup>-2<br \/>\n<\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3^2}\" alt=\"\\frac{1}{3^2}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 a<sup>-m<\/sup> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) 2<sup>-3<\/sup>\u00d7(-7)<sup> \u2013 3\u00a0<\/sup><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= (2\u00d7-7)<sup>-3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/sup>\u2235 a<sup>m<\/sup>\u00d7b<sup>m<\/sup>\u00a0= (ab)<sup>m <\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{(2\\times&amp;space;-7)^3}\" alt=\"\\frac{1}{(2\\times -7)^3}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 a<sup>-m<\/sup> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{-14^3}\" alt=\"\\frac{1}{-14^3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Find the value of: <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i)<\/strong> (3<sup>0<\/sup>+4<sup>-1<\/sup>)\u00d72<sup>2<br \/>\n<\/sup><strong>(ii)<\/strong> (2<sup>-1<\/sup>\u00d74<sup>-1<\/sup>)\u00f72<sup>\u00a0\u2013 2<br \/>\n<\/sup><strong>(iii)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{2}&amp;space;\\right&amp;space;)^{-2}&amp;space;+&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{3}&amp;space;\\right&amp;space;)^{-2}&amp;space;+&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{4}&amp;space;\\right&amp;space;)^{-2}\" alt=\"\\left ( \\frac{1}{2} \\right )^{-2} + \\left ( \\frac{1}{3} \\right )^{-2} + \\left ( \\frac{1}{4} \\right )^{-2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv)<\/strong> (3<sup>-1<\/sup>+4<sup>-1<\/sup>+5<sup>-1<\/sup>)<sup>0 <\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;\\{&amp;space;\\left&amp;space;(&amp;space;\\frac{-2}{3}&amp;space;\\right&amp;space;)^{-2}&amp;space;\\right&amp;space;\\}^2\" alt=\"\\left \\{ \\left ( \\frac{-2}{3} \\right )^{-2} \\right \\}^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i)(3<sup>0<\/sup>+4<sup>\u2013 1<\/sup>)\u00d72<sup>2<\/sup>\u00a0<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= (1 + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{4}\" alt=\"\\frac{1}{4}\" align=\"absmiddle\" \/>) \u00d7 2<sup>2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/sup>\u00a0 \u2235 a<sup>-m <\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(4+1)}{4}\" alt=\"\\frac{(4+1)}{4}\" align=\"absmiddle\" \/> \u00d7 2<sup>2 <\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{4}\" alt=\"\\frac{5}{4}\" align=\"absmiddle\" \/> \u00d7 2<sup>2 <\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{2^2}\" alt=\"\\frac{5}{2^2}\" align=\"absmiddle\" \/> \u00d7 2<sup>2<br \/>\n<\/sup>= 5 \u00d7 2 <sup>(2-2) <\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 (a)<sup>m<\/sup> \u00f7(a)<sup>n<\/sup> = a<sup>m &#8211; n<br \/>\n<\/sup>= 5\u00d72<sup>0<br \/>\n<\/sup>= 5\u00d71 = 5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) (2<sup>-1<\/sup>\u00d74<sup>-1<\/sup>)\u00f72<sup>-2<\/sup><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\\times&amp;space;\\frac{1}{4}&amp;space;\\div&amp;space;\\frac{1}{2^2}\" alt=\"\\frac{1}{2}\\times \\frac{1}{4} \\div \\frac{1}{2^2}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 a<sup>-m <\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\\times&amp;space;\\frac{1}{2^2}&amp;space;\\div&amp;space;\\frac{1}{2^2}\" alt=\"\\frac{1}{2}\\times \\frac{1}{2^2} \\div \\frac{1}{2^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2^3}&amp;space;\\div&amp;space;\\frac{1}{2^2}\" alt=\"\\frac{1}{2^3} \\div \\frac{1}{2^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2^3}&amp;space;\\times&amp;space;2^2\" alt=\"\\frac{1}{2^3} \\times 2^2\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{2}&amp;space;\\right&amp;space;)^{-2}&amp;space;+&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{3}&amp;space;\\right&amp;space;)^{-2}&amp;space;+&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{4}&amp;space;\\right&amp;space;)^{-2}\" alt=\"\\left ( \\frac{1}{2} \\right )^{-2} + \\left ( \\frac{1}{3} \\right )^{-2} + \\left ( \\frac{1}{4} \\right )^{-2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= (2<sup>-1<\/sup>)<sup>-2 <\/sup>+ (3<sup>-1<\/sup>)<sup>-2 <\/sup>+ (4<sup>-1<\/sup>)<sup>-2<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 a<sup>-m <\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2<sup>(-1\u00d7-2) <\/sup>+ 3<sup>(-1\u00d7-2) <\/sup>+ 4<sup>(-1\u00d7-2)\u00a0\u00a0<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u2235 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?(a^{m})^n&amp;space;=&amp;space;a^{m\\times&amp;space;n}\" alt=\"(a^{m})^n = a^{m\\times n}\" align=\"absmiddle\" \/><br \/>\n= 2<sup>2<\/sup>+3<sup>2<\/sup>+4<sup>2<br \/>\n<\/sup>= 4+9+16<br \/>\n= 29<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) (3<sup>-1<\/sup>+4<sup>-1<\/sup>+5<sup>-1<\/sup>)<sup>0<\/sup><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;\\{&amp;space;\\left&amp;space;(&amp;space;\\frac{-2}{3}&amp;space;\\right&amp;space;)^{-2}&amp;space;\\right&amp;space;\\}^2\" alt=\"\\left \\{ \\left ( \\frac{-2}{3} \\right )^{-2} \\right \\}^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{-2}{3}&amp;space;\\right&amp;space;)^{-4}\" alt=\"\\left ( \\frac{-2}{3} \\right )^{-4}\" align=\"absmiddle\" \/><sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/sup>\u2235 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?(a^{m})^n&amp;space;=&amp;space;a^{m\\times&amp;space;n}\" alt=\"(a^{m})^n = a^{m\\times n}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(\\frac{-3}{2}&amp;space;\\right&amp;space;)^4\" alt=\"\\left (\\frac{-3}{2} \\right )^4\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 a<sup>-m <\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{81}{16}\" alt=\"\\frac{81}{16}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Evaluate:<br \/>\n<\/strong><strong>(i)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8^{-1}\\times&amp;space;5^3}{2^{-4}}\" alt=\"\\frac{8^{-1}\\times 5^3}{2^{-4}}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii)<\/strong> (5<sup>-1<\/sup>\u00d72<sup>-2<\/sup>)\u00d76<sup>-1<\/sup>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8^{-1}\\times&amp;space;5^3}{2^{-4}}\" alt=\"\\frac{8^{-1}\\times 5^3}{2^{-4}}\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(2^3)^{-1}\\times&amp;space;5^3}{2^{-4}}\" alt=\"\\frac{(2^3)^{-1}\\times 5^3}{2^{-4}}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2^{-3}\\times&amp;space;5^3}{2^{-4}}\" alt=\"\\frac{2^{-3}\\times 5^3}{2^{-4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?(a^{m})^n&amp;space;=&amp;space;a^{m\\times&amp;space;n}\" alt=\"(a^{m})^n = a^{m\\times n}\" align=\"absmiddle\" \/><br \/>\n= 2 <sup>-3-(-4) <\/sup>\u00d7 5<sup>3\u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 (a)<sup>m<\/sup> \u00f7(a)<sup>n<\/sup> = a<sup>m &#8211; n<br \/>\n<\/sup>= 2 \u00d7 125<br \/>\n= 250<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii)<\/strong>\u00a0<strong>(5<sup>-1<\/sup>\u00d72<sup>-2<\/sup>)\u00d76<sup>-1<\/sup>\u00a0<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{5}&amp;space;\\times&amp;space;\\frac{1}{2}\\right&amp;space;)\\times&amp;space;\\frac{1}{6}\" alt=\"\\left ( \\frac{1}{5} \\times \\frac{1}{2}\\right )\\times \\frac{1}{6}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 a<sup>-m <\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{10}\\times&amp;space;\\frac{1}{6}\" alt=\"\\frac{1}{10}\\times \\frac{1}{6}\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{60}\" alt=\"\\frac{1}{60}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Find the value of\u00a0<em>m<\/em>\u00a0for which 5<em><sup>m\u00a0<\/sup><\/em>\u00f7\u00a05<sup>-3<\/sup>\u00a0= 5<sup>5<\/sup><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 5<em><sup>m<\/sup><\/em>\u00a0\u00f7 5<sup>-3<\/sup>\u00a0= 5<sup>5 <\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 5<sup>(m-(-3) )<\/sup>\u00a0= 5<sup>5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/sup>\u00a0 \u2235 (a)<sup>m<\/sup> \u00f7(a)<sup>n<\/sup> = a<sup>m &#8211; n <\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 5<sup>m+3<\/sup>\u00a0=5<sup>5<br \/>\n<\/sup>Comparing exponents on both sides, we get<br \/>\nm+3 = 5<br \/>\nm = 5 &#8211; 3<br \/>\nm = 2<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. Evaluate:<br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i)\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;\\{&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{3}&amp;space;\\right&amp;space;)^{-1}&amp;space;-&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{4}&amp;space;\\right&amp;space;)^{-1}\\right&amp;space;\\}^{-1}\" alt=\"\\left \\{ \\left ( \\frac{1}{3} \\right )^{-1} - \\left ( \\frac{1}{4} \\right )^{-1}\\right \\}^{-1}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii)\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{5}{8}&amp;space;\\right&amp;space;)^{-7}&amp;space;\\times&amp;space;\\left&amp;space;(&amp;space;\\frac{8}{5}&amp;space;\\right&amp;space;)^{-4}\" alt=\"\\left ( \\frac{5}{8} \\right )^{-7} \\times \\left ( \\frac{8}{5} \\right )^{-4}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i)\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;\\{&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{3}&amp;space;\\right&amp;space;)^{-1}&amp;space;-&amp;space;\\left&amp;space;(&amp;space;\\frac{1}{4}&amp;space;\\right&amp;space;)^{-1}\\right&amp;space;\\}^{-1}\" alt=\"\\left \\{ \\left ( \\frac{1}{3} \\right )^{-1} - \\left ( \\frac{1}{4} \\right )^{-1}\\right \\}^{-1}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;\\{&amp;space;\\left&amp;space;(&amp;space;\\frac{3}{1}&amp;space;\\right&amp;space;)^1&amp;space;-&amp;space;\\left&amp;space;(&amp;space;\\frac{4}{1}&amp;space;\\right&amp;space;)^1\\right&amp;space;\\}\" alt=\"\\left \\{ \\left ( \\frac{3}{1} \\right )^1 - \\left ( \\frac{4}{1} \\right )^1\\right \\}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 a<sup>-m <\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><br \/>\n= 3 &#8211; 4<br \/>\n= -1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{5}{8}&amp;space;\\right&amp;space;)^{-7}&amp;space;\\times&amp;space;\\left&amp;space;(&amp;space;\\frac{8}{5}&amp;space;\\right&amp;space;)^{-4}\" alt=\"\\left ( \\frac{5}{8} \\right )^{-7} \\times \\left ( \\frac{8}{5} \\right )^{-4}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5^{-7}}{8^{-7}}&amp;space;\\times&amp;space;\\frac{8^{-4}}{5^{-4}}\" alt=\"\\frac{5^{-7}}{8^{-7}} \\times \\frac{8^{-4}}{5^{-4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{a}{b}&amp;space;\\right&amp;space;)^m&amp;space;=&amp;space;\\frac{a^m}{b^m}\" alt=\"\\left ( \\frac{a}{b} \\right )^m = \\frac{a^m}{b^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= 5<sup>-7-(-4)<\/sup> \u00d7 8<sup>-4-(-7)<\/sup><img decoding=\"async\" class=\"\" title=\"NCERT Solution For Class 8 Maths Chapter 12\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/08\/ncert-solution-class-8-chapter-12-40.png\" alt=\"Ncert solution class 8 chapter 12-40\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 (a)<sup>m<\/sup> \u00f7(a)<sup>n<\/sup> = a<sup>m &#8211; n <\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\">= 5<sup>-7+4 <\/sup>\u00d7 8<sup>-4+7<\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\">= 5<sup>-3<\/sup> \u00d7 8<sup>3 <\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8^3}{5^3}\" alt=\"\\frac{8^3}{5^3}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2235 a<sup>-m <\/sup>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{a^m}\" alt=\"\\frac{1}{a^m}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{512}{125}\" alt=\"\\frac{512}{125}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>7. Simplify the following:<br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{25\\times&amp;space;t^{-4}}{5^{-3}&amp;space;\\times&amp;space;10&amp;space;\\times&amp;space;t^{-8}}\" alt=\"\\frac{25\\times t^{-4}}{5^{-3} \\times 10 \\times t^{-8}}\" align=\"absmiddle\" \/>\u00a0<\/strong>(t \u2260 0)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3^{-5}&amp;space;\\times&amp;space;10^{-5}\\times&amp;space;125}{5^{-7}\\times&amp;space;6^{-5}}\" alt=\"\\frac{3^{-5} \\times 10^{-5}\\times 125}{5^{-7}\\times 6^{-5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{25\\times&amp;space;t^{-4}}{5^{-3}&amp;space;\\times&amp;space;10&amp;space;\\times&amp;space;t^{-8}}\" alt=\"\\frac{25\\times t^{-4}}{5^{-3} \\times 10 \\times t^{-8}}\" align=\"absmiddle\" \/>\u00a0(t \u2260 0)<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5^2\\times&amp;space;t^{-4}}{5^{-3}&amp;space;\\times&amp;space;5&amp;space;\\times2\\times&amp;space;t^{-8}}\" alt=\"\\frac{5^2\\times t^{-4}}{5^{-3} \\times 5 \\times2\\times t^{-8}}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5^{2-(-3)-1}\\times&amp;space;t^{-4-(-8)}}{2}\" alt=\"\\frac{5^{2-(-3)-1}\\times t^{-4-(-8)}}{2}\" width=\"153\" height=\"42\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 (a)<sup>m<\/sup> \u00f7(a)<sup>n<\/sup> = a<sup>m &#8211; n<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5^{2+3-1}\\times&amp;space;t^{-4+8}}{2}\" alt=\"\\frac{5^{2+3-1}\\times t^{-4+8}}{2}\" align=\"absmiddle\" \/> \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5^{5}\\times&amp;space;t^{4}}{2}\" alt=\"\\frac{5^{5}\\times t^{4}}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{625t^4}{2}\" alt=\"\\frac{625t^4}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3^{-5}&amp;space;\\times&amp;space;10^{-5}\\times&amp;space;125}{5^{-7}\\times&amp;space;6^{-5}}\" alt=\"\\frac{3^{-5} \\times 10^{-5}\\times 125}{5^{-7}\\times 6^{-5}}\" width=\"133\" height=\"41\" align=\"absmiddle\" \/>\u00a0<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3^{-5}&amp;space;\\times&amp;space;(2\\times&amp;space;5)^{-5}\\times&amp;space;5^3}{5^{-7}\\times&amp;space;(2\\times&amp;space;3)^{-5}}\" alt=\"\\frac{3^{-5} \\times (2\\times 5)^{-5}\\times 5^3}{5^{-7}\\times (2\\times 3)^{-5}}\" align=\"absmiddle\" \/> \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3^{-5}&amp;space;\\times&amp;space;2^{-5}\\times&amp;space;5^{-5}\\times&amp;space;5^3}{5^{-7}\\times&amp;space;2^{-5}\\times&amp;space;3^{-5}}\" alt=\"\\frac{3^{-5} \\times 2^{-5}\\times 5^{-5}\\times 5^3}{5^{-7}\\times 2^{-5}\\times 3^{-5}}\" width=\"162\" height=\"41\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>\u2235 <\/strong>(ab)<sup>m\u00a0<\/sup>= a<sup>m<\/sup>b<sup>m<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3^{-5}&amp;space;\\times&amp;space;2^{-5}\\times&amp;space;5^{-5+3}}{5^{-7}\\times&amp;space;2^{-5}\\times&amp;space;3^{-5}}\" alt=\"\\frac{3^{-5} \\times 2^{-5}\\times 5^{-5+3}}{5^{-7}\\times 2^{-5}\\times 3^{-5}}\" width=\"140\" height=\"41\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3^{-5}&amp;space;\\times&amp;space;2^{-5}\\times&amp;space;5^{-2}}{5^{-7}\\times&amp;space;2^{-5}\\times&amp;space;3^{-5}}\" alt=\"\\frac{3^{-5} \\times 2^{-5}\\times 5^{-2}}{5^{-7}\\times 2^{-5}\\times 3^{-5}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2235 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?a^m\\times&amp;space;a^n&amp;space;=&amp;space;a^{m+n}\" alt=\"a^m\\times a^n = a^{m+n}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">= 3<sup>-5-(-5)<\/sup> \u00d7 2<sup>-5-(-5)<\/sup> \u00d7 5<sup>-2-(-7)\u00a0 \u00a0 \u00a0<\/sup> \u2235 (a)<sup>m<\/sup> \u00f7(a)<sup>n<\/sup> = a<sup>m &#8211; n<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 3 <sup>-5+5<\/sup> \u00d72 <sup>-5+5<\/sup> \u00d7 5<sup>-2+7<\/sup><\/span><br \/>\n<span style=\"color: #000000;\">= 3<sup>0<\/sup> \u00d7 2<sup>0<\/sup> \u00d7 5<sup>5\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/sup> \u2235 a<sup>0<\/sup> = 1<br \/>\n= 1 \u00d7 1 \u00d7 3125<br \/>\n= 3125<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 32px;\">\n<td style=\"width: 100%; background-color: #f2e079; text-align: center; height: 32px;\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong>NCERT Class 8<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 8 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Mathematics<\/a>\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-sanskrit-ruchira\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">NCERT Solutions Class 8 Sanskrit<\/span><\/strong><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 8 Mathematics\u00a0 Chapter &#8211; 12 (Exponents and Powers)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 12 Exponents and Powers Exercise 12.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 12: Exponents and Powers NCERT Solution Class 8 Maths Ex [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[442],"tags":[466,467,445,5],"class_list":["post-3387","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-12-exponents-and-powers-in-english","tag-ncert-solutions-class-8-maths-chapter-12-in-english","tag-ncert-solutions-class-8-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 8 Mathematics\u00a0Chapter - 12 (Exponents and Powers)\u00a0The NCERT Solutions in English Language for Class 8 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