**Exercise 12.1**

Question 1.

Evaluate:

(i) 3^{-2}

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

(iii) (1/2)^{-5}

Solution:

Question 2.

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

Solution:

Question 3.

Find the value of

Solution:

Question 4.

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} [∵ a^{m} ÷ a^{n} = a^{m-n}]

⇒ 5^{m+3} = 5^{5}

Comparing the powers of equal bases, we have

m + 3 = 5

m = 5 – 3 = 2, i.e., m = 2

Question 6.

Evaluate:

Solution:

Question 7.

Simplify:

Solution:

**Exercise 12.2**