Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $3$ by $4$ .

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

Step 2

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

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

Step 3

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

$81 x^{4}$