Question

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

• A. $\frac{4}{5}$
• B. $\frac{4}{25}$
• C. $\frac{25}{4}$
• D. $\frac{5}{2}$

Answer 1

The correct option is C

$\frac{25}{4}$

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

By using the law of exponent, ${\mathrm{a}}^{-\mathrm{m}}=\frac{1}{{\mathrm{a}}^{\mathrm{m}}}$

We have,

$\begin{array}{rcl}{\left(\frac{2}{5}\right)}^{-2}& =& \frac{1}{{\left({\displaystyle \frac{2}{5}}\right)}^2}\\ & =& \frac{1}{{\displaystyle \frac{4}{25}}}\\ & =& \frac{25}{4}\\ \therefore {\left(\frac{2}{5}\right)}^{-2}& =& \frac{25}{4}\end{array}$

Hence, the correct option is C.