Question

Simplify \[\left[ \left\{ \left( 625 \right)^{- 1/2} \right\}^{- 1/4} \right]^2\]

Answer 1

We have to simplify. `[{(625)^((-1)/2)}^((-1)/4)]^2`So,

 `[{(625)^((-1)/2)}^((-1)/4)]^2 = [{1/(625^(1/2))}^((-1)/4)\]^2`

`= [{1/5^(4 xx -1/2)}^((-1)/4)]^2`

`= [{1/5^2}^((-1)/4)]^2`

`= [{1/5^(2 xx 1/4)}]^2`

 `[{(625)^((-1)/2)}^((-1)/4)]^2`   `= [{1/5^((-1)/2)}]^2`

`[{1/(1/5^(1/2))}]`

`= [{1 xx 5^(1/2)}]^2`

`= 5^(1/2xx2)`

= 5

Hence, the value of `[{(625)^((-1)/2)}^((-1)/4)]^2`  is 5.