Algebra Examples

$5 \sqrt{x^{7}} \div \sqrt{x^{4}}$

Step 1

Rewrite the division as a fraction.

$\frac{5 \sqrt{x^{7}}}{\sqrt{x^{4}}}$

Step 2

Combine $\sqrt{x^{7}}$ and $\sqrt{x^{4}}$ into a single radical.

$5 \sqrt{\frac{x^{7}}{x^{4}}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Reduce the expression $\frac{x^{7}}{x^{4}}$ by cancelling the common factors.

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Step 3.1.1

Factor $x^{4}$ out of $x^{7}$ .

$5 \sqrt{\frac{x^{4} x^{3}}{x^{4}}}$

Step 3.1.2

Multiply by $1$ .

$5 \sqrt{\frac{x^{4} x^{3}}{x^{4} \cdot 1}}$

Step 3.1.3

Cancel the common factor.

$5 \sqrt{\frac{x^{4} x^{3}}{x^{4} \cdot 1}}$

Step 3.1.4

Rewrite the expression.

$5 \sqrt{\frac{x^{3}}{1}}$

Step 3.2

Divide $x^{3}$ by $1$ .

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

Step 4

Factor out $x^{2}$ .

$5 \sqrt{x^{2} x}$

Step 5

Pull terms out from under the radical.

$5 x \sqrt{x}$