( 243 32 )^ 4 5 #160; =( 3^ 5 2^ 5 )^ 4 5 #160; =( 3 4 )^ 4 =( 2 3 )^ 4 =( 2 3 )^ 4 = 16 81 ...

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Property 1

simplify 24...

Question

simplify ${(\frac{243}{32})}^{- \frac{4}{5}}$

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Solution

$(\frac{243}{32})^{\frac{- 4}{5}} = (\frac{3^{5}}{2^{5}})^{\frac{- 4}{5}} = (\frac{3}{4})^{- 4} = (\frac{2}{3})^{4} = (\frac{2}{3})^{4} = \frac{16}{81}$

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