Question

question 3
convert each power to radical notation.
i. $2^{\frac{1}{4}}$
ii. $6^{-\frac{1}{2}}$

Explanation:

Step1: Apply fractional exponent rule

For $a^{\frac{1}{n}}$, it equals $\sqrt[n]{a}$. So $2^{\frac{1}{4}} = \sqrt[4]{2}$

Step2: Apply negative exponent rule

First, $a^{-m}=\frac{1}{a^m}$, so $6^{-\frac{1}{2}}=\frac{1}{6^{\frac{1}{2}}}$. Then use fractional exponent rule: $6^{\frac{1}{2}}=\sqrt{6}$, so $\frac{1}{6^{\frac{1}{2}}}=\frac{1}{\sqrt{6}}$

Answer:

I. $\boldsymbol{\sqrt[4]{2}}$
II. $\boldsymbol{\frac{1}{\sqrt{6}}}$