Question

Simplify:

`(32a^-10)^(1/5) (343a^12)^(1/3)`

Answer 1

Given,

`(32a^-10)^(1/5) (343a^12)^(1/3)`

We have to simplify the given expression.

Thus, `(32a^-10)^(1/5) (343a^12)^(1/3)`

⇒ `(32)^(1/5) xx (a^-10)^(1/5) xx (343)^(1/3) xx (a^12)^(1/3)`   ...[∴ (a × b)ⁿ = aⁿ × bⁿ]

⇒ `(2^5)^(1/5) xx (a^-10)^(1/5) xx (7^3)^(1/3) xx (a^12)^(1/3)`

⇒ `(2)^(5 xx 1/5) xx (a)^(-10 xx 1/5) xx (7)^(3 xx 1/3) xx (a)^(12 xx 1/3)`   ...[∴ (aⁿ)^m = a^nm]

⇒ 2 × a^–2 × 7 × a⁴ 

⇒ 14 × a^{–2 + 4}  ...[∴ aⁿ × a^m = a^{n + m}]

⇒ 14a²

Hence, `(32a^-10)^(1/5) (343a^12)^(1/3) = 14a^2`.