# Exercise 12.1

Question 1

Evaluate

(i) 3−2 (ii) (−4)−2 (iii)

Sol :

(i)

(ii)

(iii)

Question 2

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

(i) (ii)

(iii) (iv)

(v)

Sol :

(i) (−4)5 ÷ (−4)8 = (−4)5 − 8 (am ÷ an = amn)

= (− 4)−3

(ii)

(iii)

(iv) (3− 7 ÷ 3−10) × 3−5 = (3−7 − (−10)) × 3−5 (am ÷ an = am n)

= 33 × 3−5

= 33 + (− 5) (am × an = am + n)

= 3−2

(v) 2−3 × (−7)−3 =

Question 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)

Sol :

(i)

(ii) (2−1 × 4−1) ÷ 2− 2 = [2−1 × {(2)2}− 1] ÷ 2− 2

= (2− 1 × 2− 2) ÷ 2− 2

= 2−1+ (−2) ÷ 2−2 (am × an = am + n)

= 2−3 ÷ 2−2

= 2−3 − (−2) (am ÷ an = amn)

= 2−3 + 2 = 2 −1

(iii)

(iv) (3−1 + 4−1 + 5−1)0

= 1 (a0 = 1)

(v)

Question 4

Evaluate (i) (ii)

Sol :

(i)

(ii)

Question 5

Find the value of m for which 5m ÷5−3 = 55.

Sol :

5m ÷ 5−3 = 55

5m − (− 3) = 55 (am ÷ an = amn)

5m + 3 = 55

Since the powers have same bases on both sides, their respective exponents must be equal.

m + 3 = 5

m = 5 − 3

m = 2

Question 6

Evaluate (i) (ii)

Sol :

(i)

(ii)

Question 7

Simplify. (i) (ii)

Sol :

(i)

(ii)