Find-27-2-3-1-2equal to

Given [(27)^ 2/3]^1/2[ [(27)^ 2/3]^1/2 = (27)^ 2/3×1/2; ...

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Standard IX

Mathematics

Rationalisation

Find[27-2/3]1...

Question

Find ${[{(27)}^{- \frac{2}{3}}]}^{\frac{1}{2}}$ equal to

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Solution

Given ${[{(27)}^{- \frac{2}{3}}]}^{\frac{1}{2}}$
$\begin{array}{rcl} {[{(27)}^{- \frac{2}{3}}]}^{\frac{1}{2}} & = & {(27)}^{\frac{- 2}{3} \times \frac{1}{2}} \\ = & {(27)}^{\frac{- 1}{3}} \\ = & {(\frac{1}{27})}^{\frac{1}{3}} \\ = & {(\frac{1}{3^{3}})}^{\frac{1}{3}} [∵ The cube root of 27 is 3] \\ = & \frac{1}{3} \end{array}$
$∴$ ${[{(27)}^{- \frac{2}{3}}]}^{\frac{1}{2}} = \frac{1}{3}$

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Find ${[{(27)}^{- \frac{2}{3}}]}^{\frac{1}{2}}$ equal to