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Simplify [ { ( 625 ) − 1 / 2 } − 1 / 4 ] 2 - Mathematics

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. 

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Q 12 | Page 29
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