Question

The Value of${\left(\frac{2}{5}\right)}^{-3}$ is

Answer 1

Find the value of${\left(\frac{2}{5}\right)}^{-3}$:

By using the law of exponent,

$a^{\mathit{-}\mathit{n}}\mathit{=}\frac{\mathit{1}}{{\mathit{a}}^{\mathit{n}}}$

$\begin{array}{rcl}{\left(\frac{2}{5}\right)}^{-3}& =& \frac{1}{{\left({\displaystyle \frac{2}{5}}\right)}^3}\\ & =& \frac{1}{{\displaystyle \frac{8}{125}}}\\ & =& \frac{125}{8}\\ \therefore {\left(\frac{2}{5}\right)}^{-3}& =& \frac{125}{8}\end{array}$

Hence, value of ${\left(\frac{2}{5}\right)}^{-3}$ is $\frac{125}{8}.$