Simplify ( square root of 117x^28y^27)/( square root of 13x^10y^5)

$\frac{\sqrt{117 x^{28} y^{27}}}{\sqrt{13 x^{10} y^{5}}}$

Combine $\sqrt{117 x^{28} y^{27}}$ and $\sqrt{13 x^{10} y^{5}}$ into a single radical.

$\sqrt{\frac{117 x^{28} y^{27}}{13 x^{10} y^{5}}}$

Reduce the expression $\frac{117 x^{28} y^{27}}{13 x^{10} y^{5}}$ by cancelling the common factors.

Factor $13$ out of $117 x^{28} y^{27}$ .

$\sqrt{\frac{13 (9 x^{28} y^{27})}{13 x^{10} y^{5}}}$

Factor $13$ out of $13 x^{10} y^{5}$ .

$\sqrt{\frac{13 (9 x^{28} y^{27})}{13 (x^{10} y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{13 (9 x^{28} y^{27})}{13 (x^{10} y^{5})}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{28} y^{27}}{x^{10} y^{5}}}$

Cancel the common factor of $x^{28}$ and $x^{10}$ .

Factor $x^{10}$ out of $9 x^{28} y^{27}$ .

$\sqrt{\frac{x^{10} (9 x^{18} y^{27})}{x^{10} y^{5}}}$

Cancel the common factors.

Factor $x^{10}$ out of $x^{10} y^{5}$ .

$\sqrt{\frac{x^{10} (9 x^{18} y^{27})}{x^{10} (y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{x^{10} (9 x^{18} y^{27})}{x^{10} y^{5}}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{18} y^{27}}{y^{5}}}$

Cancel the common factor of $y^{27}$ and $y^{5}$ .

Factor $y^{5}$ out of $9 x^{18} y^{27}$ .

$\sqrt{\frac{y^{5} (9 x^{18} y^{22})}{y^{5}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{y^{5} (9 x^{18} y^{22})}{y^{5} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y^{5} (9 x^{18} y^{22})}{y^{5} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{18} y^{22}}{1}}$

Divide $9 x^{18} y^{22}$ by $1$ .

$\sqrt{9 x^{18} y^{22}}$

Rewrite $9 x^{18} y^{22}$ as ${(3 x^{9} y^{11})}^{2}$ .

$\sqrt{{(3 x^{9} y^{11})}^{2}}$

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

$3 x^{9} y^{11}$