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\left(\frac{a^5\:b^{-3}}{ab}\right)^{-\frac{1}{3}}

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=\left(\frac{a^5 \cdot b^{-3}}{ab}\right)^{-\frac{1}{3}}\\
=\left(\frac{a^5}{a} \cdot b^{-3}\right)^{-\frac{1}{3}}\\
=\left(a^4 \cdot b^{-3}\right)^{-\frac{1}{3}}\\
=(a^4)^{-\frac{1}{3}} \cdot (b^{-3})^{-\frac{1}{3}}\\
=a^{-\frac{4}{3}} \cdot b^1\\
=\boxed{\frac{b}{a^{\frac{4}{3}}}}

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