Algebra Examples

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

Step 1

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

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Step 1.1

Factor out $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

Move $x$ .

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

Step 1.4

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Cancel the common factor of $y$ .

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Step 3.1

Factor $y$ out of $4 y$ .

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

Step 3.2

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

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

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

Step 4

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

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

Step 5

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

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

Step 6

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

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

Step 7

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

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

Step 8

Add $1$ and $1$ .

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

Step 9

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

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

Step 10

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

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

Step 11

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

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