Finite Math Examples

$\frac{\sqrt[3]{120 x^{15}}}{\sqrt[3]{5 x}}$

Step 1

Combine $\sqrt[3]{120 x^{15}}$ and $\sqrt[3]{5 x}$ into a single radical.

$\sqrt[3]{\frac{120 x^{15}}{5 x}}$

Step 2

Reduce the expression $\frac{120 x^{15}}{5 x}$ by cancelling the common factors.

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Step 2.1

Factor $5$ out of $120 x^{15}$ .

$\sqrt[3]{\frac{5 (24 x^{15})}{5 x}}$

Step 2.2

Factor $5$ out of $5 x$ .

$\sqrt[3]{\frac{5 (24 x^{15})}{5 (x)}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{5 (24 x^{15})}{5 x}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{24 x^{15}}{x}}$

Step 3

Cancel the common factor of $x^{15}$ and $x$ .

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Step 3.1

Factor $x$ out of $24 x^{15}$ .

$\sqrt[3]{\frac{x (24 x^{14})}{x}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt[3]{\frac{x (24 x^{14})}{x^{1}}}$

Step 3.2.2

Factor $x$ out of $x^{1}$ .

$\sqrt[3]{\frac{x (24 x^{14})}{x \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$\sqrt[3]{\frac{x (24 x^{14})}{x \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$\sqrt[3]{\frac{24 x^{14}}{1}}$

Step 3.2.5

Divide $24 x^{14}$ by $1$ .

$\sqrt[3]{24 x^{14}}$

Step 4

Rewrite $24 x^{14}$ as ${(2 x^{4})}^{3} \cdot (3 x^{2})$ .

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Step 4.1

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) x^{14}}$

Step 4.2

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} \cdot 3 x^{14}}$

Step 4.3

Factor out $x^{12}$ .

$\sqrt[3]{2^{3} \cdot 3 (x^{12} x^{2})}$

Step 4.4

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

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

Step 4.5

Move $3$ .

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

Step 4.6

Rewrite $2^{3} {(x^{4})}^{3}$ as ${(2 x^{4})}^{3}$ .

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

Step 4.7

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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