Simplify square root of (u^8)/(u^18)

$\sqrt{\frac{u^{8}}{u^{18}}}$

Reduce the expression $\frac{u^{8}}{u^{18}}$ by cancelling the common factors.

Multiply by $1$ .

$\sqrt{\frac{u^{8} \cdot 1}{u^{18}}}$

Factor $u^{8}$ out of $u^{18}$ .

$\sqrt{\frac{u^{8} \cdot 1}{u^{8} u^{10}}}$

Cancel the common factor.

$\sqrt{\frac{u^{8} \cdot 1}{u^{8} u^{10}}}$

Rewrite the expression.

$\sqrt{\frac{1}{u^{10}}}$

Simplify the expression.

Rewrite $1$ as $1^{2}$ .

$\sqrt{\frac{1^{2}}{u^{10}}}$

Rewrite $u^{10}$ as ${(u^{5})}^{2}$ .

$\sqrt{\frac{1^{2}}{{(u^{5})}^{2}}}$

Rewrite $\frac{1^{2}}{{(u^{5})}^{2}}$ as ${(\frac{1}{u^{5}})}^{2}$ .

$\sqrt{{(\frac{1}{u^{5}})}^{2}}$

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

$\frac{1}{u^{5}}$