( 81/49 )^ 3/2 = ( 49/81 )^3/2 =( 7^2/9^2 )^3/2 = [(7/9)^2]^3/2 =(7/9)^3 = 343/729 ...

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Laws of Exponents for Real Numbers

Evaluate 81/4...

Question

Evaluate ${(\frac{81}{49})}^{- \frac{3}{2}}$

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Solution

$(\frac{81}{49})^{- \frac{3}{2}} = (\frac{49}{81})^{\frac{3}{2}} = (\frac{7^{2}}{9^{2}})^{\frac{3}{2}} = [(\frac{7}{9})^{2}]^{\frac{3}{2}} = (\frac{7}{9})^{3} = \frac{343}{729}$

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127

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