You can Download KSEEB Solutions for Class 8 Maths Chapter 12 Exponents and Powers Ex 12.1 Questions and Answers helps you to revise the complete syllabus.

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

Question 1.

Evaluate.

(i) 3^{-2}

(ii) (-4)^{-2}

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

Solution:

Question 2.

Simplify and express the result in power notation with a positive exponent.

(i) (-4)^{5} ÷ (-4)^{8}

(ii) \(\left(\frac{1}{2^{3}}\right)^{2}\)

(iii) \((-3)^{4} \times\left(\frac{5}{3}\right)^{4}\)

(iv) (3^{-7} + 3^{-10}) × 3^{-5}

(v) 2^{-3} × (-7)^{-3}

Solution:

Question 3.

Find the value of:

(i) (3^{0} + 4^{-1}) × 2^{2}

(ii) (2^{-1} × 4^{-1}) ÷ 2^{-2}

(iii) \(\left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}\)

(iv) (3^{-1} + 4^{-1} + 5^{-1})^{0}

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

Solution:

Question 4.

Evaluate

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

(ii) (5^{-1} × 2^{-1}) × 6^{-1}

Solution:

Question 5.

Find the value of m for which 5^{m} ÷ 5^{-3} = 5^{5}.

Solution:

5^{m} ÷ 5^{-3} = 5^{5}.

5^{m-(-3)} = 5^{5}.

5^{m+3} = 5^{5}.

m + 3 = 5

m = 5 – 3

m = 2

Question 6.

(i) \(\left\{\left(\frac{1}{3}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\right\}^{-1}\)

(ii) \(\left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4}\)

Solution:

Question 7.

Simplify.

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

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

Solution: