Question

Solve the que in the given picture!

Answer 1

a) 20

Explanation:

when we have an exponent of an exponent, we simply multiply them for the overall exponent.

so, we actually have

a^((1/4)×12) × b^((1/3)×12) = a³b⁴ = 5000

let's find the prime factors of 5000 :

5000 ÷ 2 = 2500

2500 ÷ 2 = 1250

1250 ÷ 2 = 625

625 ÷ 3 no

625 ÷ 5 = 125

125 ÷ 5 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

so,

5000 = 2³ × 5⁴

so, a = 2, b = 5

a²b = 2²×5 = 4×5 = 20