Question

write each radical using rational exponents.
see example 1

1. \\(\sqrt{3}\\)
2. \\(\sqrt3{7}\\)
3. \\(\sqrt5{3^2}\\)
4. \\(\sqrt4{2^{-5}}\\)

Explanation:

Step1: Convert square root to exponent

For $\sqrt{3}$, use $\sqrt[n]{a}=a^{\frac{1}{n}}$, here $n=2$:
$\sqrt{3}=3^{\frac{1}{2}}$

Step2: Convert cube root to exponent

For $\sqrt[3]{7}$, use $\sqrt[n]{a}=a^{\frac{1}{n}}$, here $n=3$:
$\sqrt[3]{7}=7^{\frac{1}{3}}$

Step3: Convert 5th root to exponent

For $\sqrt[5]{3^2}$, use $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, here $n=5,m=2$:
$\sqrt[5]{3^2}=3^{\frac{2}{5}}$

Step4: Convert 4th root to exponent

For $\sqrt[4]{2^{-5}}$, use $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, here $n=4,m=-5$:
$\sqrt[4]{2^{-5}}=2^{-\frac{5}{4}}$

Answer:

1. $3^{\frac{1}{2}}$
2. $7^{\frac{1}{3}}$
3. $3^{\frac{2}{5}}$
4. $2^{-\frac{5}{4}}$