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**Prove It** I'd start by simplifying the entire expression first...

$\displaystyle \displaystyle \begin{align*} \frac{a^2 b^7}{a^3 b} &= \frac{b^6}{a} \\ &= \frac{\left[ \left( \frac{5}{8} \right) ^3 \right] ^6}{ \left( \frac{2}{5} \right)^4 } \\ &= \frac{ \left( \frac{5}{8} \right)^{18} }{ \left( \frac{2}{5} \right)^4 } \\ &= \frac{ \frac{5^{18}}{8^{18}} }{ \frac{ 2^4 }{ 5^4 } } \\ &= \frac{5^{18}}{8^{18}} \cdot \frac{5^4}{2^4} &= \frac{5^{22}}{8^{18} \cdot 2^4} \\ &= \frac{5^{22}}{ \left( 2^3 \right)^{18} \cdot 2^4 } \\ &= \frac{ 5^{22} }{ 2^{54} \cdot 2^4 } \\ &= \frac{ 5^{22} }{ 2^{58} } \end{align*} $