Algebra Examples

$\frac{\sqrt{4 x^{3} y^{3}}}{2 x^{- 1} y^{3}}$

Step 1

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Factor out $x^{2}$ .

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

Step 2.1.3

Factor out $y^{2}$ .

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

Step 2.1.4

Move $x$ .

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

Step 2.1.5

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

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

Step 2.1.6

Add parentheses.

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

Step 2.2

Pull terms out from under the radical.

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

Step 2.3

Combine exponents.

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Step 2.3.1

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

$\frac{2 (x^{1} x) y \sqrt{x y}}{2 y^{3}}$

Step 2.3.2

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

$\frac{2 (x^{1} x^{1}) y \sqrt{x y}}{2 y^{3}}$

Step 2.3.3

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

$\frac{2 x^{1 + 1} y \sqrt{x y}}{2 y^{3}}$

Step 2.3.4

Add $1$ and $1$ .

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

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $y$ and $y^{3}$ .

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $y$ out of $y^{3}$ .

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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