Simplify the Radical Expression 9^(2/4)

$9^{\frac{2}{4}}$

Step 1

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$9^{\frac{2 (1)}{4}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$9^{\frac{2 \cdot 1}{2 \cdot 2}}$

Cancel the common factor.

$9^{\frac{2 \cdot 1}{2 \cdot 2}}$

Rewrite the expression.

$9^{\frac{1}{2}}$

Step 2

Rewrite $9$ as $3^{2}$ .

${(3^{2})}^{\frac{1}{2}}$

Step 3

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

$3^{2 (\frac{1}{2})}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$3^{2 (\frac{1}{2})}$

Rewrite the expression.

$3^{1}$

Step 5

Evaluate the exponent.

$3$