Evaluate (9^(1/2))^3

${(9^{\frac{1}{2}})}^{3}$

Step 1

Simplify the expression.

Multiply the exponents in ${(9^{\frac{1}{2}})}^{3}$ .

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

$9^{\frac{1}{2} \cdot 3}$

Combine $\frac{1}{2}$ and $3$ .

$9^{\frac{3}{2}}$

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

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{3}$

Step 3

Raise $3$ to the power of $3$ .

$27$