Question

Solve: with full workings
(32/243)^-4/5​

Answer 1

`((32)/(243))^{-(4)/(5)}=39.0625`

Explanation:

Given

`((32)/(243))^{-(4)/(5)}`

Required

Solve

`((32)/(243))^{-(4)/(5)}`

Express 32 as 2^5 and 243 as 3^5

`((2^5)/(3^5))^{-(4)/(5)}`

The exponent can be expressed as 1\5 * -4

So we have:

`((2^5)/(3^5))^{(1)/(5) * -4}`

Apply law of indices:

`((2^(5*1/5))/(5^(5*1/5)))^(-4)`

`((2)/(5))^(-4)`

In indices:

`((a)/(b))^(-c) = ((b)/(a))^(c)`

So, the expression becomes

`((5)/(2))^(4)`

`((5^(4))/(2^(4)))`

`(625)/(16)`

`39.0625`

Hence:

`((32)/(243))^{-(4)/(5)}=39.0625`