Simplify square root of (y^7)/(y^21)

$\sqrt{\frac{y^{7}}{y^{21}}}$

Step 1

Reduce the expression $\frac{y^{7}}{y^{21}}$ by cancelling the common factors.

Multiply by $1$ .

$\sqrt{\frac{y^{7} \cdot 1}{y^{21}}}$

Factor $y^{7}$ out of $y^{21}$ .

$\sqrt{\frac{y^{7} \cdot 1}{y^{7} y^{14}}}$

Cancel the common factor.

$\sqrt{\frac{y^{7} \cdot 1}{y^{7} y^{14}}}$

Rewrite the expression.

$\sqrt{\frac{1}{y^{14}}}$

Step 2

Simplify the expression.

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

$\sqrt{\frac{1^{2}}{y^{14}}}$

Rewrite $y^{14}$ as ${(y^{7})}^{2}$ .

$\sqrt{\frac{1^{2}}{{(y^{7})}^{2}}}$

Step 3

Rewrite $\frac{1^{2}}{{(y^{7})}^{2}}$ as ${(\frac{1}{y^{7}})}^{2}$ .

$\sqrt{{(\frac{1}{y^{7}})}^{2}}$

Step 4

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

$\frac{1}{y^{7}}$