Question

Simplify:

`(36a^8)^((-1)/2) (125a^15)^(1/3)`

Answer 1

Given,

`(36a^8)^((-1)/2) (125a^15)^(1/3)`

We have to simplify the given expression.

Thus, `(36a^8)^((-1)/2) (125a^15)^(1/3)`

⇒ `[(36)^((-1)/2) xx (a^8)^((-1)/2)] xx [(125)^(1/3) xx (a^15)^(1/3)]`  ...[∴ (a × b)ⁿ = aⁿ × bⁿ]

⇒ `[(6^2)^((-1)/2) xx (a^8)^((-1)/2)] xx [(5^3)^(1/3) xx (a^15)^(1/3)]`  ...[∴ (aⁿ)^m = a^nm]

⇒ `[(6)^-1 xx (a^-4)] xx [(5)^1 xx (a^5)]`

⇒ `1/6 xx 5 xx (a^5) xx (a^-4)` ...`[∴ 1/a^n = a^-n]`

⇒ `5/6 xx a^(5 - 4)`   ...[∴ (aⁿ × a^m) = a^{n + m}]

⇒ `(5a)/6`

Hence, `(36a^8)^((-1)/2) (125a^15)^(1/3) = (5a)/6`.