Answer in Brief
Simplify \[\left[ \left\{ \left( 625 \right)^{- 1/2} \right\}^{- 1/4} \right]^2\]
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Solution
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.
Concept: Laws of Exponents for Real Numbers
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