Question

$multiply \sqrt[6]{5} by \sqrt[2]{5}$
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Answer 1

$\huge{\bf{\underline{\purple{\mathrm{\underline{\red{ANS}{\blue{WER}}}}}}}}$

$\frac{ \sqrt[6]{5} }{ \sqrt[2]{5} } = \frac{ ({5})^{ \frac{1}{6} } }{ ({5})^{ \frac{1}{2} } } \\ = {5}^{ \frac{1}{6} - \frac{1}{2} } \\ = {5}^{ \frac{1 - 3}{6} } \\ = {5}^{ \frac{ -2}{6} } \\ = \frac{1}{ {5}^{ \frac{2}{6} } }$

Note :

Laws of the exponents used :

$1. \: \: \: \: \: \: \: \: \: \sqrt{x} = (x {)}^{ \frac{1}{2} }$

$2. \: \: \: \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$3. \: \: \: \: \: \: {a}^{ - m} = \frac{1}{ {a}^{m} }$

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