Simplify (3 fourth root of x)^2

${(3 \sqrt[4]{x})}^{2}$

Simplify the expression.

Apply the product rule to $3 \sqrt[4]{x}$ .

$3^{2} {\sqrt[4]{x}}^{2}$

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

$9 {\sqrt[4]{x}}^{2}$

Rewrite ${\sqrt[4]{x}}^{2}$ as $\sqrt{x}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x}$ as $x^{\frac{1}{4}}$ .

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

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

$9 x^{\frac{1}{4} \cdot 2}$

Combine $\frac{1}{4}$ and $2$ .

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

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

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite $x^{\frac{1}{2}}$ as $\sqrt{x}$ .

$9 \sqrt{x}$