Basic Math Examples

$\frac{9 y}{2 u} \cdot \frac{8 u y}{3 y^{3}}$

Step 1

Combine.

$\frac{9 y (8 u y)}{2 u (3 y^{3})}$

Step 2

Multiply $y$ by $y$ by adding the exponents.

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Step 2.1

Move $y$ .

$\frac{9 (y \cdot y) (8 u)}{2 u (3 y^{3})}$

Step 2.2

Multiply $y$ by $y$ .

$\frac{9 y^{2} (8 u)}{2 u (3 y^{3})}$

$\frac{9 y^{2} (8 u)}{2 u (3 y^{3})}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $9$ and $3$ .

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Step 3.1.1

Factor $3$ out of $9 y^{2} (8 u)$ .

$\frac{3 (3 y^{2} (8 u))}{2 u (3 y^{3})}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3$ out of $2 u (3 y^{3})$ .

$\frac{3 (3 y^{2} (8 u))}{3 (2 u (y^{3}))}$

Step 3.1.2.2

Cancel the common factor.

$\frac{3 (3 y^{2} (8 u))}{3 (2 u (y^{3}))}$

Step 3.1.2.3

Rewrite the expression.

$\frac{3 y^{2} (8 u)}{2 u (y^{3})}$

$\frac{3 y^{2} (8 u)}{2 u (y^{3})}$

$\frac{3 y^{2} (8 u)}{2 u (y^{3})}$

Step 3.2

Cancel the common factor of $y^{2}$ and $y^{3}$ .

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Step 3.2.1

Factor $y^{2}$ out of $3 y^{2} (8 u)$ .

$\frac{y^{2} (3 (8 u))}{2 u (y^{3})}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $y^{2}$ out of $2 u (y^{3})$ .

$\frac{y^{2} (3 (8 u))}{y^{2} (2 u (y))}$

Step 3.2.2.2

Cancel the common factor.

$\frac{y^{2} (3 (8 u))}{y^{2} (2 u (y))}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3 (8 u)}{2 u (y)}$

$\frac{3 (8 u)}{2 u (y)}$

$\frac{3 (8 u)}{2 u (y)}$

Step 3.3

Cancel the common factor of $8$ and $2$ .

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Step 3.3.1

Factor $2$ out of $3 (8 u)$ .

$\frac{2 (3 (4 u))}{2 u (y)}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $2$ out of $2 u (y)$ .

$\frac{2 (3 (4 u))}{2 (u (y))}$

Step 3.3.2.2

Cancel the common factor.

$\frac{2 (3 (4 u))}{2 (u (y))}$

Step 3.3.2.3

Rewrite the expression.

$\frac{3 (4 u)}{u (y)}$

$\frac{3 (4 u)}{u (y)}$

$\frac{3 (4 u)}{u (y)}$

Step 3.4

Cancel the common factor of $u$ .

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Step 3.4.1

Cancel the common factor.

$\frac{3 (4 u)}{u y}$

Step 3.4.2

Rewrite the expression.

$\frac{3 \cdot (4)}{y}$

$\frac{3 \cdot (4)}{y}$

$\frac{3 \cdot (4)}{y}$

Step 4

Multiply $3$ by $4$ .

$\frac{12}{y}$

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