Algebra Examples

$4 \sqrt[4]{80 x^{5}} \div \sqrt[4]{5 x}$

Step 1

Rewrite the division as a fraction.

$\frac{4 \sqrt[4]{80 x^{5}}}{\sqrt[4]{5 x}}$

Step 2

Combine $\sqrt[4]{80 x^{5}}$ and $\sqrt[4]{5 x}$ into a single radical.

$4 \sqrt[4]{\frac{80 x^{5}}{5 x}}$

Step 3

Reduce the expression $\frac{80 x^{5}}{5 x}$ by cancelling the common factors.

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Step 3.1

Factor $5$ out of $80 x^{5}$ .

$4 \sqrt[4]{\frac{5 (16 x^{5})}{5 x}}$

Step 3.2

Factor $5$ out of $5 x$ .

$4 \sqrt[4]{\frac{5 (16 x^{5})}{5 (x)}}$

Step 3.3

Cancel the common factor.

$4 \sqrt[4]{\frac{5 (16 x^{5})}{5 x}}$

Step 3.4

Rewrite the expression.

$4 \sqrt[4]{\frac{16 x^{5}}{x}}$

Step 4

Cancel the common factor of $x^{5}$ and $x$ .

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Step 4.1

Factor $x$ out of $16 x^{5}$ .

$4 \sqrt[4]{\frac{x (16 x^{4})}{x}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$4 \sqrt[4]{\frac{x (16 x^{4})}{x^{1}}}$

Step 4.2.2

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

$4 \sqrt[4]{\frac{x (16 x^{4})}{x \cdot 1}}$

Step 4.2.3

Cancel the common factor.

$4 \sqrt[4]{\frac{x (16 x^{4})}{x \cdot 1}}$

Step 4.2.4

Rewrite the expression.

$4 \sqrt[4]{\frac{16 x^{4}}{1}}$

Step 4.2.5

Divide $16 x^{4}$ by $1$ .

$4 \sqrt[4]{16 x^{4}}$

Step 5

Rewrite $16 x^{4}$ as ${(2 x)}^{4}$ .

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

Step 6

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

$4 (2 x)$

Step 7

Multiply $2$ by $4$ .

$8 x$