Question

Simplify and write each of the following in exponential form:

(i) (25)³ ÷ 5³

(ii) (81)⁵ ÷ (3²)⁵

(iii) 9⁸ × (x²)⁵/ (27)⁴ × (x³)²

(iv) 3² × 7⁸ × 13⁶/ 21² × 91³

Answer 1

(i) Given (25)³ ÷ 5³

= (5²)³ ÷ 5³[According to the law of exponents we have (a^m)ⁿ = a^mn]

= 5⁶ ÷ 5³ [According to the law of exponents we have a^m ÷ aⁿ = a^m-n]         

= 5^{6 – 3}

= 5³

(ii) Given (81)⁵ ÷ (3²)⁵[According to the law of exponents we have (a^m)ⁿ = a^mn]

= (81)⁵ ÷ 3¹⁰[81 = 3⁴]

= (3⁴)⁵ ÷ 3¹⁰ [According to the law of exponents we have (a^m)ⁿ = a^mn]

= 3²⁰ ÷ 3¹⁰

= 3^20-10 [According to the law of exponents we have a^m ÷ aⁿ = a^m-n]         

= 3¹⁰

(iii) Given 9⁸ × (x²)⁵/ (27)⁴ × (x³)²

= (3²)⁸ × (x²)⁵/ (3³)⁴× (x³)²[According to the law of exponents we have (a^m)ⁿ = a^mn]

= 3¹⁶ × x¹⁰/3¹² × x⁶

= 3^16-12 × x^10-6[According to the law of exponents we have a^m ÷ aⁿ = a^m-n]         

= 3⁴ × x⁴

= (3x)⁴

(iv) Given (3² × 7⁸ × 13⁶)/ (21² × 91³)

= (3² × 7²7⁸ × 13⁶)/(21²× 13³ × 7³)[According to the law of exponents we have (a^m)ⁿ = a^mn]

= (21² × 7² × 13⁶)/(21²× 13³ × 7³)

= (7⁶ × 13⁶)/(13³ × 7³)

= 91⁶/91³[According to the law of exponents we have a^m ÷ aⁿ = a^m-n] 

= 91^6-3

= 91³