Question

Simplify and express each of the following in exponential form:

(i) {(2³)⁴ × 28} ÷ 2¹²

(ii) (8² × 8⁴) ÷ 8³

(iii) (5⁷/5²) × 5³

(iv) (5⁴× x¹⁰y⁵)/ (5⁴ × x⁷y⁴)

Answer 1

(i) Given {(2³)⁴ × 28} ÷ 2¹²

{(2³)⁴ x 2⁸} ÷ 2¹²= {2¹² x 2⁸} ÷ 2¹² [According to the law of exponents we have (a^m)ⁿ = a^mn]

= 2^{(12 + 8)} ÷ 2¹²[According to the law of exponents we have a^m x aⁿ = a^{(m +n)}]

= 2²⁰ ÷ 2¹² [According to the law of exponents we have a^m ÷ aⁿ = a^m-n]         

= 2 ^{(20 – 12)} 

=  2⁸

(ii) Given (8² × 8⁴) ÷ 8³

(8² × 8⁴) ÷ 8³ [According to the law of exponents we have a^m x aⁿ = a^{(m +n)}]

= 8^{(2 + 4)} ÷ 8³

= 8⁶ ÷ 8³[According to the law of exponents we have a^m ÷ aⁿ = a^m-n]   

= 8^(6-3) = 8³ = (2³)³ = 2⁹

(iii) Given (5⁷/5²) × 5³

= 5^(7-2) x 5³[According to the law of exponents we have a^m ÷ aⁿ = a^m-n]         

= 5⁵ x 5³[According to the law of exponents we have a^m x aⁿ = a^{(m +n)}]

= 5^{(5 + 3)} 

= 5⁸

(iv) Given (5⁴× x¹⁰y⁵)/ (5⁴ × x⁷y⁴)

= (5^4-4× x^10-7y^5-4) [According to the law of exponents we have a^m ÷ aⁿ = a^m-n]         

= 5⁰x³y¹ [since 5⁰ = 1]

= 1x³y