Simplify (3x)/(4y) square root of x^3y^4

$\frac{3 x}{4 y} \sqrt{x^{3} y^{4}}$

Rewrite $x^{3} y^{4}$ as ${(x y^{2})}^{2} x$ .

Factor out $x^{2}$ .

$\frac{3 x}{4 y} \cdot \sqrt{x^{2} x y^{4}}$

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

$\frac{3 x}{4 y} \cdot \sqrt{x^{2} x {(y^{2})}^{2}}$

Move $x$ .

$\frac{3 x}{4 y} \cdot \sqrt{x^{2} {(y^{2})}^{2} x}$

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

$\frac{3 x}{4 y} \cdot \sqrt{{(x y^{2})}^{2} x}$

Pull terms out from under the radical.

$\frac{3 x}{4 y} \cdot (x y^{2} \sqrt{x})$

Cancel the common factor of $y$ .

Factor $y$ out of $4 y$ .

$\frac{3 x}{y \cdot 4} \cdot (x y^{2} \sqrt{x})$

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

$\frac{3 x}{y \cdot 4} \cdot (y (x y \sqrt{x}))$

Cancel the common factor.

$\frac{3 x}{y \cdot 4} \cdot (y (x y \sqrt{x}))$

Rewrite the expression.

$\frac{3 x}{4} \cdot (x y \sqrt{x})$

Combine $x$ and $\frac{3 x}{4}$ .

$\frac{x (3 x)}{4} \cdot (y \sqrt{x})$

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

$\frac{3 (x^{1} x)}{4} \cdot (y \sqrt{x})$

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

$\frac{3 (x^{1} x^{1})}{4} \cdot (y \sqrt{x})$

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

$\frac{3 x^{1 + 1}}{4} \cdot (y \sqrt{x})$

Add $1$ and $1$ .

$\frac{3 x^{2}}{4} \cdot (y \sqrt{x})$

Combine $y$ and $\frac{3 x^{2}}{4}$ .

$\frac{y (3 x^{2})}{4} \cdot \sqrt{x}$

Combine $\frac{y (3 x^{2})}{4}$ and $\sqrt{x}$ .

$\frac{y (3 x^{2}) \sqrt{x}}{4}$

Move $3$ to the left of $y$ .

$\frac{3 y x^{2} \sqrt{x}}{4}$