Question

rewrite the expression using radical notation.

1. $5^{3/4}$
2. $3^{1/5}$
3. $4^2$

Explanation:

Step1: Apply rational exponent rule

Recall $a^{m/n} = \sqrt[n]{a^m}$. For $5^{3/4}$:
$\sqrt[4]{5^3}$

Step2: Apply rational exponent rule

For $3^{1/5}$:
$\sqrt[5]{3^1} = \sqrt[5]{3}$

Step3: Apply exponent to radical rule

For $4^2$, since $4^2 = (4^2)^{1/1} = \sqrt[1]{4^2}$, but a 1st root is the number itself, or we can write it as $\sqrt{4^4}$ (simpler to use the direct radical form for integer exponent as $\sqrt[1]{4^2}$ or just note integer exponents can be written as 1st root, but standardly:
$\sqrt[1]{4^2} = 4^2$, but the radical form equivalent is $\sqrt{4^4}$ is not needed; correct radical form for integer exponent is $\sqrt[1]{4^2}$, but more naturally, since $a^k = \sqrt[1]{a^k}$, so:
$\sqrt[1]{4^2}$

Answer:

1. $\sqrt[4]{5^3}$
2. $\sqrt[5]{3}$
3. $\sqrt[1]{4^2}$ (or equivalently $4^2$ as a 1st radical is the base itself)