Algebra Examples

${(\sqrt[3]{x^{4}})}^{5}$

Step 1

Factor out $x^{3}$ .

${\sqrt[3]{x^{3} x}}^{5}$

Step 2

Pull terms out from under the radical.

${(x \sqrt[3]{x})}^{5}$

Step 3

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

$x^{5} {\sqrt[3]{x}}^{5}$

Step 4

Rewrite ${\sqrt[3]{x}}^{5}$ as $\sqrt[3]{x^{5}}$ .

$x^{5} \sqrt[3]{x^{5}}$

Step 5

Factor out $x^{3}$ .

$x^{5} \sqrt[3]{x^{3} x^{2}}$

Step 6

Pull terms out from under the radical.

$x^{5} (x \sqrt[3]{x^{2}})$

Step 7

Multiply $x^{5}$ by $x$ by adding the exponents.

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Step 7.1

Move $x$ .

$x \cdot x^{5} \sqrt[3]{x^{2}}$

Step 7.2

Multiply $x$ by $x^{5}$ .

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Step 7.2.1

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

$x^{1} x^{5} \sqrt[3]{x^{2}}$

Step 7.2.2

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

$x^{1 + 5} \sqrt[3]{x^{2}}$

Step 7.3

Add $1$ and $5$ .

$x^{6} \sqrt[3]{x^{2}}$