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Simplify each of the following:$ \frac{\sqrt[4]{1250}}{\sqrt[4]{2}} $
Given:
\( \frac{\sqrt[4]{1250}}{\sqrt[4]{2}} \)
To do:
We have to simplify the given expression.
Solution:
We know that,
$(a^{m})^{n}=a^{m n}$
$a^{m} \times a^{n}=a^{m+n}$
$a^{m} \div a^{n}=a^{m-n}$
$\sqrt[n]{a} \times \sqrt[n]{b}=\sqrt[n]{a \times b}$
$\sqrt[n]{a} \div \sqrt[n]{b}=\sqrt[n]{\frac{a}{b}}$
$a^{0}=1$
Therefore,
$\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}=\sqrt[4]{\frac{1250}{2}}$
$=\sqrt[4]{625}$
$=\sqrt[4]{5 \times 5 \times 5 \times 5}$
$=(5^{4})^{\frac{1}{4}}$
$=5^{4 \times \frac{1}{4}}$
$=5^{1}$
$=5$
Hence, $\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}=5$.
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