Processing math: 100%

Simplify ( square root of x^12)/( square root of x^5)

$\frac{\sqrt{x^{12}}}{\sqrt{x^{5}}}$

Step 1

Combine

$\sqrt{x^{12}}$ and

$\sqrt{x^{5}}$ into a single radical.

$\sqrt{\frac{x^{12}}{x^{5}}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression

$\frac{x^{12}}{x^{5}}$ by cancelling the common factors.

Factor

$x^{5}$ out of

$x^{12}$ .

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

Multiply by

$1$ .

$\sqrt{\frac{x^{5} x^{7}}{x^{5} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{5} x^{7}}{x^{5} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{x^{7}}{1}}$

Divide

$x^{7}$ by

$1$ .

$\sqrt{x^{7}}$

Step 3

Rewrite

$x^{7}$ as

${(x^{3})}^{2} x$ .

Factor out

$x^{6}$ .

$\sqrt{x^{6} x}$

Rewrite

$x^{6}$ as

${(x^{3})}^{2}$ .

$\sqrt{{(x^{3})}^{2} x}$

Step 4

Pull terms out from under the radical.

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