Question

Simplify:

`(81a^8)^((-3)/4) (8a^15)^(2/3)`

Answer 1

Given,

`(81a^8)^((-3)/4) (8a^15)^(2/3)`

We have to simplify the given expression.

Thus, `(81a^8)^((-3)/4) (8a^15)^(2/3)`

⇒ `(81)^((-3)/4) xx (a^8)^((-3)/4) xx (8)^(2/3) xx (a^15)^(2/3)`  ...[∴ (a × b)ⁿ = aⁿ × bⁿ]

⇒ `(3^4)^((-3)/4) xx (a^8)^((-3)/4) xx (2^3)^(2/3) xx (a^15)^(2/3)`

⇒ `(3)^(4 xx (-3)/4) xx (a)^(8 xx (-3)/4) xx (2)^(3 xx 2/3) xx (a)^(15 xx 2/3)`  ...[∴ (aⁿ)^m = a^nm]

⇒ `(3)^-3 xx  (a)^-6 xx (2)^2 xx (a)^10`

⇒ `1/3^3 xx (a)^-6 xx 4 xx (a)^10`  ...`[∴ 1/a^n = a^-n]`

⇒ `4/27 xx (a)^(-6 + 10)`  ...[∴ (aⁿ × a^m) = a^{n + m}]

⇒ `(4a^4)/27`

Hence, `(81a^8)^((-3)/4) (8a^15)^(2/3) = (4a^4)/27`.