Algebra Examples

$\frac{4 w^{2} v^{3} \cdot 10 w^{7} v^{2}}{- 5 w v^{4}} + 14 w^{8} v$

Step 1

Simplify each term.

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Step 1.1

Multiply $w^{2}$ by $w^{7}$ by adding the exponents.

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Step 1.1.1

Move $w^{7}$ .

$\frac{4 (w^{7} w^{2}) v^{3} \cdot (10 v^{2})}{- 5 w v^{4}} + 14 w^{8} v$

Step 1.1.2

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

$\frac{4 w^{7 + 2} v^{3} \cdot (10 v^{2})}{- 5 w v^{4}} + 14 w^{8} v$

Step 1.1.3

Add $7$ and $2$ .

$\frac{4 w^{9} v^{3} \cdot (10 v^{2})}{- 5 w v^{4}} + 14 w^{8} v$

Step 1.2

Multiply $v^{3}$ by $v^{2}$ by adding the exponents.

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Step 1.2.1

Move $v^{2}$ .

$\frac{4 w^{9} (v^{2} v^{3}) \cdot 10}{- 5 w v^{4}} + 14 w^{8} v$

Step 1.2.2

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

$\frac{4 w^{9} v^{2 + 3} \cdot 10}{- 5 w v^{4}} + 14 w^{8} v$

Step 1.2.3

Add $2$ and $3$ .

$\frac{4 w^{9} v^{5} \cdot 10}{- 5 w v^{4}} + 14 w^{8} v$

Step 1.3

Cancel the common factor of $w^{9}$ and $w$ .

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Step 1.3.1

Factor $w$ out of $4 w^{9} v^{5} \cdot 10$ .

$\frac{w (4 w^{8} v^{5} \cdot 10)}{- 5 w v^{4}} + 14 w^{8} v$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $w$ out of $- 5 w v^{4}$ .

$\frac{w (4 w^{8} v^{5} \cdot 10)}{w (- 5 v^{4})} + 14 w^{8} v$

Step 1.3.2.2

Cancel the common factor.

$\frac{w (4 w^{8} v^{5} \cdot 10)}{w (- 5 v^{4})} + 14 w^{8} v$

Step 1.3.2.3

Rewrite the expression.

$\frac{4 w^{8} v^{5} \cdot 10}{- 5 v^{4}} + 14 w^{8} v$

Step 1.4

Cancel the common factor of $v^{5}$ and $v^{4}$ .

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Step 1.4.1

Factor $v^{4}$ out of $4 w^{8} v^{5} \cdot 10$ .

$\frac{v^{4} (4 w^{8} v \cdot 10)}{- 5 v^{4}} + 14 w^{8} v$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $v^{4}$ out of $- 5 v^{4}$ .

$\frac{v^{4} (4 w^{8} v \cdot 10)}{v^{4} \cdot - 5} + 14 w^{8} v$

Step 1.4.2.2

Cancel the common factor.

$\frac{v^{4} (4 w^{8} v \cdot 10)}{v^{4} \cdot - 5} + 14 w^{8} v$

Step 1.4.2.3

Rewrite the expression.

$\frac{4 w^{8} v \cdot 10}{- 5} + 14 w^{8} v$

Step 1.5

Cancel the common factor of $10$ and $- 5$ .

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Step 1.5.1

Factor $5$ out of $4 w^{8} v \cdot 10$ .

$\frac{5 (4 w^{8} v \cdot 2)}{- 5} + 14 w^{8} v$

Step 1.5.2

Move the negative one from the denominator of $\frac{4 w^{8} v \cdot 2}{- 1}$ .

$- 1 \cdot (4 w^{8} v \cdot 2) + 14 w^{8} v$

Step 1.6

Rewrite $- 1 \cdot (4 w^{8} v \cdot 2)$ as $- (4 w^{8} v \cdot 2)$ .

$- (4 w^{8} v \cdot 2) + 14 w^{8} v$

Step 1.7

Multiply $2$ by $4$ .

$- (8 w^{8} v) + 14 w^{8} v$

Step 1.8

Multiply $8$ by $- 1$ .

$- 8 w^{8} v + 14 w^{8} v$

Step 2

Add $- 8 w^{8} v$ and $14 w^{8} v$ .

$6 w^{8} v$