Question

Simplify:

`(8/125)^(1/3)[(4/9)^(-1/2) ÷ (2/5)^2]`

Answer 1

Given,

`(8/125)^(1/3)[(4/9)^(-1/2) ÷ (2/5)^2]`

We need to simplify the given terms.

Thus, `(8/125)^(1/3)[(4/9)^(-1/2) ÷ (2/5)^2]`

⇒ `(2^3/5^3)^(1/3) [(2^2/3^2)^(-1/2) ÷ (2/5)^2]`

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

⇒ `(2/5) [(2/3)^-1 ÷ (2/5)^2]`

⇒ `(2/5) [3/2 xx 5/2 xx 5/2]`  ...`[∵ (a/b)^-n = (b/a)^n, a/b ÷ c/d = a/b xx d/c]`

⇒ `2/5 xx 3/2 xx 5/2 xx 5/2`

= `15/4`

= `3 3/4`

Hence, the required is `3 3/4`.