Simplify:$ \left(\frac{\sqrt{2}}{5}\right)^{8} \p\left(\frac{\sqrt{2}}{5}\right)^{13} $

Given:

\( \left(\frac{\sqrt{2}}{5}\right)^{8} \div\left(\frac{\sqrt{2}}{5}\right)^{13} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$(\frac{\sqrt{2}}{5})^{8} \div(\frac{\sqrt{2}}{5})^{13}=(\frac{\sqrt{2}}{5})^{8-13}$

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

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

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

$=\frac{5^{5}}{2^{\frac{5}{2}}}$

$=\frac{3125}{2^2 \times \sqrt{2}}$

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

Hence, $(\frac{\sqrt{2}}{5})^{8} \div(\frac{\sqrt{2}}{5})^{13}=\frac{3125}{4 \sqrt{2}}$.

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Updated on: 10-Oct-2022

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