Simplify ( fourth root of x^4y^6* square root of x^6)/y

$\frac{\sqrt[4]{x^{4} y^{6}} \cdot \sqrt{x^{6}}}{y}$

Step 1

Simplify the numerator.

Rewrite $x^{4} y^{6}$ as ${(x y)}^{4} y^{2}$ .

Factor out $y^{4}$ .

$\frac{\sqrt[4]{x^{4} (y^{4} y^{2})} \sqrt{x^{6}}}{y}$

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

$\frac{\sqrt[4]{{(x y)}^{4} y^{2}} \sqrt{x^{6}}}{y}$

Pull terms out from under the radical.

$\frac{x y \sqrt[4]{y^{2}} \sqrt{x^{6}}}{y}$

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$\frac{x y \sqrt{\sqrt{y^{2}}} \sqrt{x^{6}}}{y}$

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

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

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

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

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

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{x^{3} x^{1} y \sqrt{y}}{y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{3 + 1} y \sqrt{y}}{y}$

Add $3$ and $1$ .

$\frac{x^{4} y \sqrt{y}}{y}$

Step 2

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{x^{4} y \sqrt{y}}{y}$

Divide $x^{4} \sqrt{y}$ by $1$ .

$x^{4} \sqrt{y}$