What is ((9^3)/(6^3))^{-1/3} ?

The solution to ((9^3)/(6^3))^{-1/3} is 2/3

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simplify ((9^3)/(6^3))^{-1/3}

simplify

(\frac{9 ^{3}}{6 ^{3}})^{- \frac{1}{3}}

\frac{2}{3}

Solution steps

(\frac{9 ^{3}}{6 ^{3}})^{- \frac{1}{3}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(\frac{9 ^{3}}{6 ^{3}})^{- \frac{1}{3}} = \frac{1}{( \frac{9 ^{3}}{6 ^{3}} ) ^{\frac{1}{3}}}

= \frac{1}{( \frac{9 ^{3}}{6 ^{3}} ) ^{\frac{1}{3}}}

(\frac{9 ^{3}}{6 ^{3}})^{\frac{1}{3}} = \frac{3}{2}

= \frac{1}{\frac{3}{2}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{2}{3}

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