Simplify the following and write the answer in exponential form.(i) 32

1.	Simplify the following and write the answer in exponential form.(i) 32 x 34 x 38(ii) 615 ÷ 610(iii) a3 x a2(iv) 7x x 72(v) (52)3 ÷ 53
Answer» (i) 3² x 3⁴ x 3² = 3²⁺⁴⁺⁸ = 3¹⁴ [∵ a^m x aⁿ = a^m+n] So 3² x 3⁴ x 3² = 3¹⁴ (ii) 6¹⁵ ÷ 6¹⁰ = 6^15-10 = 6⁵ [∵ a^m x aⁿ = a^m-n] (iii) a³ x a² = a³⁺² = a⁵ (iv) 7^x x 7² = 7^x+2 (v) (5²)³ ÷ 5³ = 5^{2 x 3} ÷ 5³ = 5⁶ ÷ 5³ [∵ (a^m)ⁿ = a^{m x n}]

Simplify the following and write the answer in exponential form.(i) 32 x 34 x 38(ii) 615 ÷ 610(iii) a3 x a2(iv) 7x x 72(v) (52)3 ÷ 53

Answer»

(i) 3² x 3⁴ x 3² = 3²⁺⁴⁺⁸

= 3¹⁴

[∵ a^m x aⁿ = a^m+n]

So 3² x 3⁴ x 3² = 3¹⁴

(ii) 6¹⁵ ÷ 6¹⁰ = 6^15-10

= 6⁵

[∵ a^m x aⁿ = a^m-n]

(iii) a³ x a² = a³⁺²

= a⁵

(iv) 7^x x 7² = 7^x+2

(v) (5²)³ ÷ 5³

= 5^{2 x 3} ÷ 5³

= 5⁶ ÷ 5³

[∵ (a^m)ⁿ = a^{m x n}]