What is ((a^2b)/3)^{-3} ?

The solution to ((a^2b)/3)^{-3} is (27)/(a^6b^3)

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simplify ((a^2b)/3)^{-3}

simplify

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

\frac{27}{a ^{6} b ^{3}}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(\frac{a ^{2} b}{3})^{3} : \frac{a ^{6} b ^{3}}{27}

= \frac{1}{\frac{a ^{6} b ^{3}}{27}}

Apply the fraction rule:

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

= \frac{27}{a ^{6} b ^{3}}

\frac{8 x ^{2}}{2 x ^{2}}

\frac{5}{6} \cdot \frac{7}{8}

10 (\frac{1}{2})

\frac{4 x ^{3}}{x ^{3}}

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