Question

find the value of (64/125)raised to the power of -2/3 + 1/(256/625)raised to the power of 1/4 + root 25 / cube root 64

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ {\left(\frac{64}{125}\right)}^{\frac{-2}{3}}+{\left(\frac{625}{256}\right)}^{\frac{1}{4}}+\frac{\sqrt{25}}{\sqrt[3]{64}} \\ \mathrm{On}\mathrm{simplyfing} \\ \Rightarrow {\left(\frac{4^3}{5^3}\right)}^{\frac{-2}{3}}+{\left(\frac{5^4}{4^4}\right)}^{\frac{1}{4}}+\frac{\sqrt{5^2}}{\sqrt[3]{4^3}} \\ \Rightarrow {\left(\frac{4}{5}\right)}^{\frac{-2\times 3}{3}}+{\left(\frac{5}{4}\right)}^{\frac{1\times 4}{4}}+\frac{5^{{\displaystyle \frac{2}{2}}}}{4^{{\displaystyle \frac{3}{3}}}} \\ \Rightarrow {\left(\frac{4}{5}\right)}^{-2}+\left(\frac{5}{4}\right)+\frac{5}{4} \\ \Rightarrow {\left(\frac{5}{4}\right)}^2+\frac{5}{4}+\frac{5}{4} \\ \Rightarrow \frac{25}{16}+\frac{10}{4} \\ \Rightarrow \frac{65}{16}\mathrm{Ans} \end{gathered}$$