Algebra Examples

$\frac{\frac{\frac{11 - w}{30 w^{2}}}{w - 11}}{5 w^{6}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{11 - w}{30 w^{2}}}{w - 11} \cdot \frac{1}{5 w^{6}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{11 - w}{30 w^{2}} \cdot \frac{1}{w - 11} \frac{1}{5 w^{6}}$

Step 3

Multiply $\frac{11 - w}{30 w^{2}}$ by $\frac{1}{w - 11}$ .

$\frac{11 - w}{30 w^{2} (w - 11)} \cdot \frac{1}{5 w^{6}}$

Step 4

Cancel the common factor of $11 - w$ and $w - 11$ .

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Step 4.1

Rewrite $11$ as $- 1 (- 11)$ .

$\frac{- 1 (- 11) - w}{30 w^{2} (w - 11)} \cdot \frac{1}{5 w^{6}}$

Step 4.2

Factor $- 1$ out of $- w$ .

$\frac{- 1 (- 11) - (w)}{30 w^{2} (w - 11)} \cdot \frac{1}{5 w^{6}}$

Step 4.3

Factor $- 1$ out of $- 1 (- 11) - (w)$ .

$\frac{- 1 (- 11 + w)}{30 w^{2} (w - 11)} \cdot \frac{1}{5 w^{6}}$

Step 4.4

Reorder terms.

$\frac{- 1 (w - 11)}{30 w^{2} (w - 11)} \cdot \frac{1}{5 w^{6}}$

Step 4.5

Cancel the common factor.

$\frac{- 1 (w - 11)}{30 w^{2} (w - 11)} \cdot \frac{1}{5 w^{6}}$

Step 4.6

Rewrite the expression.

$\frac{- 1}{30 w^{2}} \cdot \frac{1}{5 w^{6}}$

Step 5

Combine.

$\frac{- 1 \cdot 1}{30 w^{2} (5 w^{6})}$

Step 6

Multiply $w^{2}$ by $w^{6}$ by adding the exponents.

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Step 6.1

Move $w^{6}$ .

$\frac{- 1 \cdot 1}{30 (w^{6} w^{2}) \cdot 5}$

Step 6.2

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

$\frac{- 1 \cdot 1}{30 w^{6 + 2} \cdot 5}$

Step 6.3

Add $6$ and $2$ .

$\frac{- 1 \cdot 1}{30 w^{8} \cdot 5}$

Step 7

Multiply $- 1$ by $1$ .

$\frac{- 1}{30 w^{8} \cdot 5}$

Step 8

Multiply $5$ by $30$ .

$\frac{- 1}{150 w^{8}}$

Step 9

Move the negative in front of the fraction.

$- \frac{1}{150 w^{8}}$