Basic Math Examples

$\frac{\sqrt{80 x^{11}}}{\sqrt{5 x}}$

Step 1

Combine $\sqrt{80 x^{11}}$ and $\sqrt{5 x}$ into a single radical.

$\sqrt{\frac{80 x^{11}}{5 x}}$

Step 2

Reduce the expression $\frac{80 x^{11}}{5 x}$ by cancelling the common factors.

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Step 2.1

Factor $5$ out of $80 x^{11}$ .

$\sqrt{\frac{5 (16 x^{11})}{5 x}}$

Step 2.2

Factor $5$ out of $5 x$ .

$\sqrt{\frac{5 (16 x^{11})}{5 (x)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{5 (16 x^{11})}{5 x}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{16 x^{11}}{x}}$

Step 3

Cancel the common factor of $x^{11}$ and $x$ .

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Step 3.1

Factor $x$ out of $16 x^{11}$ .

$\sqrt{\frac{x (16 x^{10})}{x}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt{\frac{x (16 x^{10})}{x^{1}}}$

Step 3.2.2

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

$\sqrt{\frac{x (16 x^{10})}{x \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$\sqrt{\frac{x (16 x^{10})}{x \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$\sqrt{\frac{16 x^{10}}{1}}$

Step 3.2.5

Divide $16 x^{10}$ by $1$ .

$\sqrt{16 x^{10}}$

Step 4

Rewrite $16 x^{10}$ as ${(4 x^{5})}^{2}$ .

$\sqrt{{(4 x^{5})}^{2}}$

Step 5

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

$4 x^{5}$