Question

Simplify and express in exponential form:

${\left(\frac{3}{7}\right)}^5\times {\left(\frac{2}{5}\right)}^5$.

Answer 1

Given: ${\left(\frac{3}{7}\right)}^5\times {\left(\frac{2}{5}\right)}^5$.

$$\begin{gathered} {\left(\frac{3}{7}\right)}^5\times {\left(\frac{2}{5}\right)}^5={\left(\frac{3}{7}\times \frac{2}{5}\right)}^5\left[\because {\mathrm{a}}^{\mathrm{m}}\times {\mathrm{b}}^{\mathrm{m}}={\left(\mathrm{ab}\right)}^{\mathrm{m}}\right] \\ ={\left(\frac{6}{35}\right)}^5 \end{gathered}$$

Hence, the exponential form of ${\left(\frac{3}{7}\right)}^5\times {\left(\frac{2}{5}\right)}^5$ is ${\left(\frac{6}{35}\right)}^5$.