Evaluate (n root of a)^n

${(\sqrt[n]{a})}^{n}$

Step 1

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

${(a^{\frac{1}{n}})}^{n}$

Step 2

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

$a^{\frac{1}{n} n}$

Step 3

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

$a^{\frac{n}{n}}$

Step 4

Cancel the common factor of $n$ .

Cancel the common factor.

$a^{\frac{n}{n}}$

Rewrite the expression.

$a^{1}$

Step 5

Simplify.

$a$