Simplify the Radical Expression cube root of (27x^3)^4

$\sqrt[3]{{(27 x^{3})}^{4}}$

Apply the product rule to $27 x^{3}$ .

$\sqrt[3]{27^{4} {(x^{3})}^{4}}$

Raise $27$ to the power of $4$ .

$\sqrt[3]{531441 {(x^{3})}^{4}}$

Multiply the exponents in ${(x^{3})}^{4}$ .

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

$\sqrt[3]{531441 x^{3 \cdot 4}}$

Multiply $3$ by $4$ .

$\sqrt[3]{531441 x^{12}}$

Rewrite $531441 x^{12}$ as ${(81 x^{4})}^{3}$ .

$\sqrt[3]{{(81 x^{4})}^{3}}$

Pull terms out from under the radical.

$81 x^{4}$