Question

Using laws of exponents, simplify and write the answer in exponential form

(i) 2³ × 2⁴ × 2⁵

(ii) 5¹² ÷ 5³

(iii) (7²)³

Answer 1

(i) Given 2³ × 2⁴ × 2⁵

We know that first law of exponents states that a^m × aⁿ × a^p = a^(m+n+p)

Therefore above equation can be written as 2³ x 2⁴ x 2⁵ = 2^{(3 + 4 + 5)} 

= 2¹²

(ii) Given 5¹² ÷ 5³

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

Therefore given question can be written as 5¹² ÷ 5³ = 5^{12 – 3} = 5⁹ 

(iii) Given (7²)³

According to the law of exponents we have (a^m)ⁿ = a^mn

Therefore given question can be written as (7²)³ = 7⁶