Evaluate (9^2)^(1/4)

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

Step 1

Simplify the expression.

Multiply the exponents in ${(9^{2})}^{\frac{1}{4}}$ .

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{1}$

Step 3

Evaluate the exponent.

$3$