Simplify ( square root of x^5y^4)/(y^2 fifth root of z^10)

$\frac{\sqrt{x^{5}} y^{4}}{y^{2} \sqrt[5]{z^{10}}}$

Step 1

Cancel the common factor of $y^{4}$ and $y^{2}$ .

Factor $y^{2}$ out of $\sqrt{x^{5}} y^{4}$ .

$\frac{y^{2} (\sqrt{x^{5}} y^{2})}{y^{2} \sqrt[5]{z^{10}}}$

Cancel the common factors.

Factor $y^{2}$ out of $y^{2} \sqrt[5]{z^{10}}$ .

$\frac{y^{2} (\sqrt{x^{5}} y^{2})}{y^{2} (\sqrt[5]{z^{10}})}$

Cancel the common factor.

$\frac{y^{2} (\sqrt{x^{5}} y^{2})}{y^{2} \sqrt[5]{z^{10}}}$

Rewrite the expression.

$\frac{\sqrt{x^{5}} y^{2}}{\sqrt[5]{z^{10}}}$

Step 2

Simplify the numerator.

Rewrite $x^{5}$ as ${(x^{2})}^{2} x$ .

Factor out $x^{4}$ .

$\frac{\sqrt{x^{4} x} y^{2}}{\sqrt[5]{z^{10}}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\frac{\sqrt{{(x^{2})}^{2} x} y^{2}}{\sqrt[5]{z^{10}}}$

Pull terms out from under the radical.

$\frac{x^{2} \sqrt{x} y^{2}}{\sqrt[5]{z^{10}}}$

Step 3

Simplify the denominator.

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

$\frac{x^{2} \sqrt{x} y^{2}}{\sqrt[5]{{(z^{2})}^{5}}}$

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

$\frac{x^{2} \sqrt{x} y^{2}}{z^{2}}$