Question

simplify the following (256/625)^-3/4

Answer 1

Dear Student


$$\begin{gathered} {\left(\frac{256}{625}\right)}^{-\frac{3}{4}}={\left[{\left(\frac{4}{5}\right)}^4\right]}^{\frac{-3}{4}} \\ \Rightarrow {\left(\frac{4}{5}\right)}^{4\times \frac{-3}{4}} \\ \Rightarrow {\left(\frac{4}{5}\right)}^{-3} \\ \Rightarrow {\left(\frac{5}{4}\right)}^3(a^{-m}=\frac{1}{a^m}) \\ \Rightarrow \frac{5\times 5\times 5}{4\times 4\times 4}=\frac{125}{64} \end{gathered}$$

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