Basic Math Examples

$\frac{2 u^{4} v^{0} \cdot (4 u^{- 5} v^{5})}{- 4 u^{- 1} v^{4}}$

Step 1

Multiply $u^{4}$ by $u^{- 5}$ by adding the exponents.

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Step 1.1

Move $u^{- 5}$ .

$\frac{2 (u^{- 5} u^{4}) v^{0} \cdot (4 v^{5})}{- 4 u^{- 1} v^{4}}$

Step 1.2

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

$\frac{2 u^{- 5 + 4} v^{0} \cdot (4 v^{5})}{- 4 u^{- 1} v^{4}}$

Step 1.3

Add $- 5$ and $4$ .

$\frac{2 u^{- 1} v^{0} \cdot (4 v^{5})}{- 4 u^{- 1} v^{4}}$

Step 2

Simplify $2 u^{- 1} v^{0} \cdot (4 v^{5})$ .

$\frac{2 u^{- 1} \cdot (4 v^{5})}{- 4 u^{- 1} v^{4}}$

Step 3

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

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Step 3.1

Factor $2$ out of $2 u^{- 1} \cdot (4 v^{5})$ .

$\frac{2 (u^{- 1} \cdot (4 v^{5}))}{- 4 u^{- 1} v^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $- 4 u^{- 1} v^{4}$ .

$\frac{2 (u^{- 1} \cdot (4 v^{5}))}{2 (- 2 u^{- 1} v^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (u^{- 1} \cdot (4 v^{5}))}{2 (- 2 u^{- 1} v^{4})}$

Step 3.2.3

Rewrite the expression.

$\frac{u^{- 1} \cdot (4 v^{5})}{- 2 u^{- 1} v^{4}}$

Step 4

Cancel the common factor of $u^{- 1}$ .

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Step 4.1

Cancel the common factor.

$\frac{u^{- 1} \cdot (4 v^{5})}{- 2 u^{- 1} v^{4}}$

Step 4.2

Rewrite the expression.

$\frac{4 v^{5}}{- 2 v^{4}}$

Step 5

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

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Step 5.1

Factor $2$ out of $4 v^{5}$ .

$\frac{2 (2 v^{5})}{- 2 v^{4}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $- 2 v^{4}$ .

$\frac{2 (2 v^{5})}{2 (- v^{4})}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (2 v^{5})}{2 (- v^{4})}$

Step 5.2.3

Rewrite the expression.

$\frac{2 v^{5}}{- v^{4}}$

Step 6

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

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Step 6.1

Factor $v^{4}$ out of $2 v^{5}$ .

$\frac{v^{4} (2 v)}{- v^{4}}$

Step 6.2

Move the negative one from the denominator of $\frac{2 v}{- 1}$ .

$- 1 \cdot (2 v)$

Step 7

Simplify the expression.

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Step 7.1

Rewrite $- 1 \cdot (2 v)$ as $- (2 v)$ .

$- (2 v)$

Step 7.2

Multiply $2$ by $- 1$ .

$- 2 v$