Simplify the Radical Expression ( cube root of 4x^3)^3

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

Reorder $4$ and $x^{3}$ .

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

Pull terms out from under the radical.

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

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

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

Rewrite ${\sqrt[3]{4}}^{3}$ as $4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4}$ as $4^{\frac{1}{3}}$ .

$x^{3} {(4^{\frac{1}{3}})}^{3}$

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

$x^{3} \cdot 4^{\frac{1}{3} \cdot 3}$

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

$x^{3} \cdot 4^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{3} \cdot 4^{\frac{3}{3}}$

Rewrite the expression.

$x^{3} \cdot 4^{1}$

Evaluate the exponent.

$x^{3} \cdot 4$

Move $4$ to the left of $x^{3}$ .

$4 x^{3}$