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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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