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

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

Apply the product rule to $3 x^{\frac{1}{2}}$ .

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

Raise $3$ to the power of $2$ .

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$9 x^{1}$

Simplify.

$9 x$