Algebra Examples

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

Step 1

Combine.

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

Step 2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

Multiply $x^{2}$ by $x$ .

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Step 2.2.1

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

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

Step 2.2.2

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

$\frac{x^{2 + 1} y \cdot 2}{4 y^{3}}$

$\frac{x^{2 + 1} y \cdot 2}{4 y^{3}}$

Step 2.3

Add $2$ and $1$ .

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

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

Step 3

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

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Step 3.1

Factor $y$ out of $x^{3} y \cdot 2$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y$ out of $4 y^{3}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

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

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

Step 4

Cancel the common factor of $2$ and $4$ .

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Step 4.1

Factor $2$ out of $x^{3} \cdot 2$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $4 y^{2}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

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