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

The solution to (-a^3*b^3)^{(-2)/3} is 1/(a^2b^2)

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

simplify

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

\frac{1}{a ^{2} b ^{2}}

Solution steps

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

Apply the fraction rule:

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

\frac{- 2}{3} = - \frac{2}{3}

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

Apply exponent rule:

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

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

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

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

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

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

= \frac{1}{a ^{2} b ^{2}}

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