Algebra Examples

$\frac{8 x^{2} y}{{(4 x y)}^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $4 x y$ .

$\frac{8 x^{2} y}{{(4 x)}^{2} y^{2}}$

Step 1.2

Apply the product rule to $4 x$ .

$\frac{8 x^{2} y}{4^{2} x^{2} y^{2}}$

Step 1.3

Raise $4$ to the power of $2$ .

$\frac{8 x^{2} y}{16 x^{2} y^{2}}$

$\frac{8 x^{2} y}{16 x^{2} y^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $8$ and $16$ .

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Step 2.1.1

Factor $8$ out of $8 x^{2} y$ .

$\frac{8 (x^{2} y)}{16 x^{2} y^{2}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $8$ out of $16 x^{2} y^{2}$ .

$\frac{8 (x^{2} y)}{8 (2 x^{2} y^{2})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{8 (x^{2} y)}{8 (2 x^{2} y^{2})}$

Step 2.1.2.3

Rewrite the expression.

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

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

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

Step 2.2

Cancel the common factor of $x^{2}$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

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

Step 2.3

Cancel the common factor of $y$ and $y^{2}$ .

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Step 2.3.1

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

$\frac{y^{1}}{2 y^{2}}$

Step 2.3.2

Factor $y$ out of $y^{1}$ .

$\frac{y \cdot 1}{2 y^{2}}$

Step 2.3.3

Cancel the common factors.

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Step 2.3.3.1

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

$\frac{y \cdot 1}{y (2 y)}$

Step 2.3.3.2

Cancel the common factor.

$\frac{y \cdot 1}{y (2 y)}$

Step 2.3.3.3

Rewrite the expression.

$\frac{1}{2 y}$

$\frac{1}{2 y}$

$\frac{1}{2 y}$

$\frac{1}{2 y}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$