-54-6×549=59(-6+9) =593=125729 [am×an=a(m+n) where a≠0]

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${(- \frac{5}{4})}^{- 6} \times {(\frac{5}{4})}^{9} = ?$

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$- \frac{5}{4}$

$\frac{25}{16}$

$\frac{5}{4}$

$\frac{125}{729}$

answer is A.

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Detailed Solution

$\begin{matrix} {(- \frac{5}{4})}^{- 6} \times {(\frac{5}{4})}^{9} = {(\frac{5}{9})}^{(- 6 + 9)} \\ = {(\frac{5}{9})}^{3} = \frac{125}{729} \\ [a^{m} \times a^{n} = a^{(m + n)} w h e r e a \neq 0] \end{matrix}$

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