Simplify (x^(1/2))^4 cube root of x^3

${(x^{\frac{1}{2}})}^{4} \sqrt[3]{x^{3}}$

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

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

$x^{\frac{1}{2} \cdot 4} \sqrt[3]{x^{3}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x^{\frac{1}{2} \cdot (2 (2))} \sqrt[3]{x^{3}}$

Cancel the common factor.

$x^{\frac{1}{2} \cdot (2 \cdot 2)} \sqrt[3]{x^{3}}$

Rewrite the expression.

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

Pull terms out from under the radical, assuming real numbers.

$x^{2} x$

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{2} x^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 1}$

Add $2$ and $1$ .

$x^{3}$