We have (((625)^ 1/2)^ 1/4)^2 =(625)^ 1/2× 1/4× 20ex0ex=(625)^1/40ex0ex=√(625)0ex0ex=√(5× 5× 5× 5)0ex0ex=5Hence (((625)^ 1/2)^ 1/4)^2=5 ...

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Fractional Exponent

625-1/2-1/42

Question

$(({{{(625)}^{- \frac{1}{2}})}^{\frac{- 1}{4}})}^{2}$

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Solution

We have- $(({{{(625)}^{- \frac{1}{2}})}^{\frac{- 1}{4}})}^{2}$
$= {(625)}^{\frac{- 1}{2} \times \frac{- 1}{4} \times 2} = {(625)}^{\frac{1}{4}} = \sqrt[4]{625} = \sqrt[4]{5 \times 5 \times 5 \times 5} = 5$
Hence- $(({{{(625)}^{- \frac{1}{2}})}^{\frac{- 1}{4}})}^{2}$ $= 5$

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