NCERT Solutions Class 8 Mathematics
Chapter – 12 (Exponents and Powers)
The NCERT Solutions in English Language for Class 8 Mathematics Chapter – 12 Exponents and Powers Exercise 12.1 has been provided here to help the students in solving the questions from this exercise.
Chapter 12: Exponents and Powers
Exercise – 12.1
1. Evaluate:
(i) 3-2
(ii) (-4)-2
(iii)
Solution –
(i) 3-2
=
=
(ii) (-4)-2
=
=
(iii)
=
= 25
= 32
2. Simplify and express the result in power notation with a positive exponent:
(i) (-4)4 ÷(-4)8
(ii)
(iii) -(3)4×
(iv) (3-7÷3-10)×3-5
(v) 2-3×(-7)-3
Solution –
(i) (-4)4 ÷(-4)8
= (-4) 5 – 8 ∵ (a)m ÷(a)n = a m – n
= (-4)–3
=
=
(ii)
=
=
=
(iii) – (3)4 ×
= (-3) 4 ×
= (-1)4 × 34 ×
= 1 × 3(4 – 4) × 54
= 3(4-4)×54 ∵ (a)m ÷(a)n = am – n
= 30×54 = 54 ∵ a0 = 1
(iv) (3-7÷3-10)×3-5
= 3 -7 – (-10) × 3-5 ∵ (a)m ÷(a)n = am – n
= 3(-7+10)×3-5
= 33×3-5
= 3(3-5)
= 3-2
=
(v) 2-3×(-7) – 3
= (2×-7)-3 ∵ am×bm = (ab)m
=
=
3. Find the value of:
(i) (30+4-1)×22
(ii) (2-1×4-1)÷2 – 2
(iii)
(iv) (3-1+4-1+5-1)0
(v)
Solution –
(i)(30+4– 1)×22
= (1 +
=
=
=
= 5 × 2 (2-2) ∵ (a)m ÷(a)n = am – n
= 5×20
= 5×1 = 5
(ii) (2-1×4-1)÷2-2
=
=
=
=
=
(iii)
= (2-1)-2 + (3-1)-2 + (4-1)-2 ∵ a-m =
= 2(-1×-2) + 3(-1×-2) + 4(-1×-2) ∵
= 22+32+42
= 4+9+16
= 29
(iv) (3-1+4-1+5-1)0
= 1
(v)
=
=
=
4. Evaluate:
(i)
(ii) (5-1×2-2)×6-1
Solution –
(i)
=
=
= 2 -3-(-4) × 53 ∵ (a)m ÷(a)n = am – n
= 2 × 125
= 250
(ii) (5-1×2-2)×6-1
=
=
=
5. Find the value of m for which 5m ÷ 5-3 = 55
Solution –
⇒ 5m ÷ 5-3 = 55
⇒ 5(m-(-3) ) = 55 ∵ (a)m ÷(a)n = am – n
⇒ 5m+3 =55
Comparing exponents on both sides, we get
m+3 = 5
m = 5 – 3
m = 2
6. Evaluate:
(i)
(ii)
Solution –
(i)
=
= 3 – 4
= -1
(ii)
=
= 5-7-(-4) × 8-4-(-7)
= 5-7+4 × 8-4+7
= 5-3 × 83
=
=
7. Simplify the following:
(i)
(ii)
Solution –
(i)
=
=
=
=
=
(ii)
=
=
=
=
= 3-5-(-5) × 2-5-(-5) × 5-2-(-7) ∵ (a)m ÷(a)n = am – n
= 3 -5+5 ×2 -5+5 × 5-2+7
= 30 × 20 × 55 ∵ a0 = 1
= 1 × 1 × 3125
= 3125