# NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1

These NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Exercise 12.1

Question 1.
Evaluate
(i) 3-2
(ii) (-4)-2
(iii) $$\left(\frac{1}{2}\right)^{-5}$$
(i) 3-2 = $$\frac{1}{3^{2}}=\frac{1}{9}$$
(ii) (-4)-2 = $$\frac{1}{(-4)^{2}}=\frac{1}{16}$$

Question 2.
Simplify and express the result in power notation with positive exponent.
(i) (-4)5 ÷ (-4)8
(ii) $$\left(\frac{1}{2^{3}}\right)^{2}$$
(iii) (-3)4 × $$\left(\frac{5}{3}\right)^{4}$$
(iv) (3-7 ÷ 310) × 3-5
(v) 2-3 × (-7)-3

Question 3.
Find the value of
(i) (3° + 4-1) × 22
(ii) (2-1 × 4-1) ÷ 2-2
(iii) $$\left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-4}$$
(iv) (3-1 + -1 + 5-1)0
(v) $$\left\{\left(\frac{-2}{3}\right)^{-2}\right\}^{2}$$
(i) (3° + 4-1) × 22
= (1 + $$\frac{1}{4}$$ ) × 22
[(i) a0 = 1 (ii) a-m = $$\frac{1}{a^{m}}$$ ]
= $$\left(\frac{4+1}{4}\right)$$ × 4 = $$\frac{5}{4}$$ × 4 = 5

Question 4.
Evaluate:
(i) $$\frac{8^{-1} \times 5^{3}}{2^{-4}}$$
(ii) (5-1 × 2-1) × 6-1
$$\frac{8^{-1} \times 5^{3}}{2^{-4}}=\frac{5^{3} \times 2^{4}}{8^{1}}=\frac{(5 \times 5 \times 5) \times 2^{4}}{2^{3}}$$
= 125 × 24-3 = 125 × 21 = 250

(ii) (5-1 × 2-1) × 6-1 = $$\left(\frac{1}{5} \times \frac{1}{2}\right) \times \frac{1}{6}$$
[a-m = $$\frac{1}{\mathrm{a}^{\mathrm{m}}}$$ ]
= $$\frac{1}{10} \times \frac{1}{6}=\frac{1}{60}$$

Question 5.
Find the value of m for which 5m ÷ 5 3 = 55.
5m ÷ 5-3 = 55
5m ÷ $$\frac{1}{5^{3}}$$ = 55
5m × 53 = 55
5m+3 = 55 (am × an = am+n)
∴ m + 3 = 5 (since the bases are equal, the exponents are equal)
m = 5 – 3
m = 2
The value of m = 2.

Question 6.
Evaluate
(i) $$\left\{\left(\frac{1}{3}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\right\}^{-1}$$
(ii) $$\left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4}$$
(i) $$\frac{25 \times \mathrm{t}^{-4}}{5^{-3} \times 10 \times \mathrm{t}^{-8}}(\mathrm{t} \neq 0)$$
(ii) $$\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}$$