Question

Simplify:

vi. ${\left(\frac{\sqrt{2}}{5}\right)}^8÷{\left(\frac{\sqrt{2}}{5}\right)}^{13}$

Answer 1

To simplify: ${\left(\frac{\sqrt{2}}{5}\right)}^8÷{\left(\frac{\sqrt{2}}{5}\right)}^{13}$

$={\left(\frac{\sqrt{2}}{5}\right)}^{8-13}$ $\{\because \frac{a^m}{a^n}=a^{m-n}\}$

$={\left(\frac{\sqrt{2}}{5}\right)}^{-5}$

$={\left(\frac{5}{\sqrt{2}}\right)}^5$ $\{\because {\left(\frac{a}{b}\right)}^{-m}={\left(\frac{b}{a}\right)}^m\}$

$=\frac{5^5}{(\sqrt{2}{)}^5}$

$=\frac{3125}{4\sqrt{2}}$

Therefore, ${\left(\frac{\sqrt{2}}{5}\right)}^8÷{\left(\frac{\sqrt{2}}{5}\right)}^{13}=\frac{3125}{4\sqrt{2}}$