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) \(\left(\frac{1}{2}\right)^{-5}\)

Answer:

(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} ÷ 3^{10}) × 3^{-5}

(v) 2^{-3} × (-7)-3

Answer:

Question 3.

Find the value of

(i) (3° + 4^{-1}) × 2^{2}

(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) \(\left\{\left(\frac{-2}{3}\right)^{-2}\right\}^{2}\)

Answer:

(i) (3° + 4^{-1}) × 2^{2}

= (1 + \(\frac{1}{4}\) ) × 2^{2}

[(i) a^{0} = 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}

Answer:

\(\frac{8^{-1} \times 5^{3}}{2^{-4}}=\frac{5^{3} \times 2^{4}}{8^{1}}=\frac{(5 \times 5 \times 5) \times 2^{4}}{2^{3}}\)

= 125 × 2^{4-3} = 125 × 2^{1} = 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.

Answer:

5^{m} ÷ 5^{-3} = 5^{5}

5^{m} ÷ \(\frac{1}{5^{3}}\) = 5^{5}

5^{m} × 5^{3} = 5^{5}

5^{m+3} = 5^{5} (a^{m} × a^{n} = a^{m+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) \(\left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4}\)

Answer:

Question 7.

Simplify:

(i) \(\frac{25 \times \mathrm{t}^{-4}}{5^{-3} \times 10 \times \mathrm{t}^{-8}}(\mathrm{t} \neq 0)\)

(ii) \(\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}\)

Answer: