Question

Simplify and express in exponential form:

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

Answer 1

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

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

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