Question

Fill in the blanks.

${\left(0.00032\right)}^{-\frac{2}{5}}=\mathrm{.......}$

Answer 1

Simplify the given expression using the law of radical exponent.

$\begin{array}{l}{\left(0.00032\right)}^{-\frac{2}{5}}\\ ={\left(\frac{32}{100000}\right)}^{-\frac{2}{5}}\\ ={\left\{\left(\frac{2^5}{{10}^5}\right)\right\}}^{-\frac{2}{5}}\\ ={\left\{{\left(\frac{2}{10}\right)}^5\right\}}^{-\frac{2}{5}}\\ ={\left(\frac{2}{10}\right)}^{5\times -\frac{2}{5}}\left[\because {\left(a^m\right)}^n=a^{mn}\right]\\ ={\left(\frac{2}{10}\right)}^{-2}\\ ={\left(\frac{10}{2}\right)}^2\left[\because a^{-n}=\frac{1}{a^n}\right]\\ =\frac{100}{4}\\ =25\end{array}$

Hence, ${\left(0.00032\right)}^{-\frac{2}{5}}=\underset{¯}{25}$