What is (\sqrt[-3]{(-27x)/(xy^3)})^3 ?

The solution to (\sqrt[-3]{(-27x)/(xy^3)})^3 is -(y^3)/(27)

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simplify (\sqrt[-3]{(-27x)/(xy^3)})^3

simplify

- \frac{y ^{3}}{27}

Solution steps

Apply radical rule:

= ((\frac{- 27 x}{x y ^{3}})^{\frac{1}{- 3}})^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (\frac{- 27 x}{x y ^{3}})^{\frac{1}{- 3} \cdot 3}

\frac{1}{- 3} \cdot 3 = - 1

= (\frac{- 27 x}{x y ^{3}})^{- 1}

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

= (- \frac{27}{y ^{3}})^{- 1}

Apply exponent rule:

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

= \frac{1}{- \frac{27}{y ^{3}}}

Apply the fraction rule:

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

= - \frac{1}{\frac{27}{y ^{3}}}

Apply the fraction rule:

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

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

= - \frac{y ^{3}}{27}

\frac{x ^{2}}{( x ^{2} + 1 ) ^{2}}

e^{2} e^{x}

2.5 \times 1 0^{- 2}

6.8 \cdot 1 0^{- 4}

What is (\sqrt[-3]{(-27x)/(xy^3)})^3 ?
The solution to (\sqrt[-3]{(-27x)/(xy^3)})^3 is -(y^3)/(27)