What is ((3x^4)/y)^{-3} ?

The solution to ((3x^4)/y)^{-3} is (y^3)/(27x^{12)}

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simplify ((3x^4)/y)^{-3}

simplify

(\frac{3 x ^{4}}{y})^{- 3}

\frac{y ^{3}}{27 x ^{12}}

Solution steps

(\frac{3 x ^{4}}{y})^{- 3}

Apply exponent rule:

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

(\frac{3 x ^{4}}{y})^{- 3} = \frac{1}{( \frac{3 x ^{4}}{y} ) ^{3}}

= \frac{1}{( \frac{3 x ^{4}}{y} ) ^{3}}

Simplify

(\frac{3 x ^{4}}{y})^{3} : \frac{27 x ^{12}}{y ^{3}}

= \frac{1}{\frac{27 x ^{12}}{y ^{3}}}

Apply the fraction rule:

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

= \frac{y ^{3}}{27 x ^{12}}

3 (\frac{1}{3} a b^{2})^{3}

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