Algebra Examples

$2 x y^{- 2} \sqrt{4 x y^{2}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 x \frac{1}{y^{2}} \sqrt{4 x y^{2}}$

Step 2

Multiply $2 x \frac{1}{y^{2}}$ .

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Step 2.1

Combine $2$ and $\frac{1}{y^{2}}$ .

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

Step 2.2

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

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

Step 3

Move $2$ to the left of $x$ .

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

Step 4

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

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Step 4.1

Rewrite $4$ as $2^{2}$ .

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

Step 4.2

Move $x$ .

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

Step 4.3

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Rewrite using the commutative property of multiplication.

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

Step 7

Multiply $2 \frac{2 x}{y^{2}}$ .

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Step 7.1

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

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

Step 7.2

Multiply $2$ by $2$ .

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

Step 8

Cancel the common factor of $y$ .

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Step 8.1

Factor $y$ out of $y^{2}$ .

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

Step 8.2

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

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

Step 8.3

Cancel the common factor.

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

Step 8.4

Rewrite the expression.

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

Step 9

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

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