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 $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

Move $x$ .

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

Step 1.4

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Remove non-negative terms from the absolute value.

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

Step 4

Cancel the common factor of $y$ .

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Step 4.1

Factor $y$ out of $4 y$ .

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

Step 4.2

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

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

Step 4.3

Cancel the common factor.

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

Step 4.4

Rewrite the expression.

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

Step 5

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

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

Step 6

Combine $| x |$ and $\frac{y (3 x)}{4}$ .

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

Step 7

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

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

Step 8

Remove unnecessary parentheses.

$\frac{| x | y \cdot 3 x \sqrt{x}}{4}$

Step 9

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

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

Step 10

Reorder factors in $\frac{3 | x | y x \sqrt{x}}{4}$ .

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