Basic Math Examples

$\frac{3 w^{2} y^{2}}{2 w^{- 1} \cdot (4 y w^{2})}$

Step 1

Multiply $w^{- 1}$ by $w^{2}$ by adding the exponents.

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Step 1.1

Move $w^{2}$ .

$\frac{3 w^{2} y^{2}}{2 (w^{2} w^{- 1}) \cdot (4 y)}$

Step 1.2

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

$\frac{3 w^{2} y^{2}}{2 w^{2 - 1} \cdot (4 y)}$

Step 1.3

Subtract $1$ from $2$ .

$\frac{3 w^{2} y^{2}}{2 w^{1} \cdot (4 y)}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Simplify $2 w^{1} \cdot (4 y)$ .

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

Step 2.2

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

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Step 2.2.1

Factor $w$ out of $3 w^{2} y^{2}$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $w$ out of $2 w \cdot (4 y)$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 2.3

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

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Step 2.3.1

Factor $y$ out of $3 w y^{2}$ .

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

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $y$ out of $2 \cdot (4 y)$ .

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

Step 2.3.2.2

Cancel the common factor.

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

Step 2.3.2.3

Rewrite the expression.

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

Step 3

Multiply $2$ by $4$ .

$\frac{3 w y}{8}$