Question

rewrite the expression using rational exponent notation.

1. $sqrt6{7}$
2. $sqrt{15}$
3. $sqrt7{14^{2}}$

Explanation:

Step1: Convert 6th root to exponent

Recall that $\sqrt[n]{a}=a^{\frac{1}{n}}$. For $\sqrt[6]{7}$, $n=6$, $a=7$.
$\sqrt[6]{7}=7^{\frac{1}{6}}$

Step2: Convert square root to exponent

A square root is a 2nd root, so $\sqrt{a}=a^{\frac{1}{2}}$. For $\sqrt{15}$, $n=2$, $a=15$.
$\sqrt{15}=15^{\frac{1}{2}}$

Step3: Convert 7th root of power to exponent

Use $\sqrt[n]{a^m}=a^{\frac{m}{n}}$. For $\sqrt[7]{14^2}$, $n=7$, $m=2$, $a=14$.
$\sqrt[7]{14^2}=14^{\frac{2}{7}}$

Answer:

1. $7^{\frac{1}{6}}$
2. $15^{\frac{1}{2}}$
3. $14^{\frac{2}{7}}$