Simplify the Radical Expression ( fifth root of 3)^5

${(\sqrt[5]{3})}^{5}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{3}$ as $3^{\frac{1}{5}}$ .

${(3^{\frac{1}{5}})}^{5}$

Step 2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{\frac{1}{5} \cdot 5}$

Step 3

Combine $\frac{1}{5}$ and $5$ .

$3^{\frac{5}{5}}$

Step 4

Cancel the common factor of $5$ .

Cancel the common factor.

$3^{\frac{5}{5}}$

Rewrite the expression.

$3^{1}$

Step 5

Evaluate the exponent.

$3$