Algebra Examples

$\frac{\sqrt[3]{270 x^{20}}}{\sqrt[3]{5 x}}$

Step 1

Combine $\sqrt[3]{270 x^{20}}$ and $\sqrt[3]{5 x}$ into a single radical.

$\sqrt[3]{\frac{270 x^{20}}{5 x}}$

Step 2

Reduce the expression $\frac{270 x^{20}}{5 x}$ by cancelling the common factors.

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Step 2.1

Factor $5$ out of $270 x^{20}$ .

$\sqrt[3]{\frac{5 (54 x^{20})}{5 x}}$

Step 2.2

Factor $5$ out of $5 x$ .

$\sqrt[3]{\frac{5 (54 x^{20})}{5 (x)}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{5 (54 x^{20})}{5 x}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{54 x^{20}}{x}}$

Step 3

Cancel the common factor of $x^{20}$ and $x$ .

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Step 3.1

Factor $x$ out of $54 x^{20}$ .

$\sqrt[3]{\frac{x (54 x^{19})}{x}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt[3]{\frac{x (54 x^{19})}{x^{1}}}$

Step 3.2.2

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

$\sqrt[3]{\frac{x (54 x^{19})}{x \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$\sqrt[3]{\frac{x (54 x^{19})}{x \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$\sqrt[3]{\frac{54 x^{19}}{1}}$

Step 3.2.5

Divide $54 x^{19}$ by $1$ .

$\sqrt[3]{54 x^{19}}$

Step 4

Rewrite $54 x^{19}$ as ${(3 x^{6})}^{3} \cdot (2 x)$ .

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Step 4.1

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) x^{19}}$

Step 4.2

Rewrite $27$ as $3^{3}$ .

$\sqrt[3]{3^{3} \cdot 2 x^{19}}$

Step 4.3

Factor out $x^{18}$ .

$\sqrt[3]{3^{3} \cdot 2 (x^{18} x)}$

Step 4.4

Rewrite $x^{18}$ as ${(x^{6})}^{3}$ .

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

Step 4.5

Move $2$ .

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

Step 4.6

Rewrite $3^{3} {(x^{6})}^{3}$ as ${(3 x^{6})}^{3}$ .

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

Step 4.7

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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