Finite Math Examples

$4 v^{- 7} x^{- 9} x^{8} v \cdot (7 u^{- 5}) \cdot (2 u^{6})$

Step 1

Multiply $v^{- 7}$ by $v$ by adding the exponents.

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Step 1.1

Move $v$ .

$4 (v \cdot v^{- 7}) x^{- 9} x^{8} \cdot (7 u^{- 5}) \cdot (2 u^{6})$

Step 1.2

Multiply $v$ by $v^{- 7}$ .

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Step 1.2.1

Raise $v$ to the power of $1$ .

$4 (v^{1} v^{- 7}) x^{- 9} x^{8} \cdot (7 u^{- 5}) \cdot (2 u^{6})$

Step 1.2.2

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

$4 v^{1 - 7} x^{- 9} x^{8} \cdot (7 u^{- 5}) \cdot (2 u^{6})$

Step 1.3

Subtract $7$ from $1$ .

$4 v^{- 6} x^{- 9} x^{8} \cdot (7 u^{- 5}) \cdot (2 u^{6})$

Step 2

Multiply $x^{- 9}$ by $x^{8}$ by adding the exponents.

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Step 2.1

Move $x^{8}$ .

$4 v^{- 6} (x^{8} x^{- 9}) \cdot (7 u^{- 5}) \cdot (2 u^{6})$

Step 2.2

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

$4 v^{- 6} x^{8 - 9} \cdot (7 u^{- 5}) \cdot (2 u^{6})$

Step 2.3

Subtract $9$ from $8$ .

$4 v^{- 6} x^{- 1} \cdot (7 u^{- 5}) \cdot (2 u^{6})$

Step 3

Multiply $u^{- 5}$ by $u^{6}$ by adding the exponents.

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Step 3.1

Move $u^{6}$ .

$4 v^{- 6} x^{- 1} \cdot (7 (u^{6} u^{- 5})) \cdot 2$

Step 3.2

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

$4 v^{- 6} x^{- 1} \cdot (7 u^{6 - 5}) \cdot 2$

Step 3.3

Subtract $5$ from $6$ .

$4 v^{- 6} x^{- 1} \cdot (7 u^{1}) \cdot 2$

Step 4

Simplify $4 v^{- 6} x^{- 1} \cdot (7 u^{1}) \cdot 2$ .

$4 v^{- 6} x^{- 1} \cdot (7 u) \cdot 2$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 \frac{1}{v^{6}} x^{- 1} \cdot (7 u) \cdot 2$

Step 6

Combine $4$ and $\frac{1}{v^{6}}$ .

$\frac{4}{v^{6}} x^{- 1} \cdot (7 u) \cdot 2$

Step 7

Rewrite using the commutative property of multiplication.

$7 \frac{4}{v^{6}} x^{- 1} u \cdot 2$

Step 8

Multiply $7 \frac{4}{v^{6}}$ .

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Step 8.1

Combine $7$ and $\frac{4}{v^{6}}$ .

$\frac{7 \cdot 4}{v^{6}} x^{- 1} u \cdot 2$

Step 8.2

Multiply $7$ by $4$ .

$\frac{28}{v^{6}} x^{- 1} u \cdot 2$

Step 9

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{28}{v^{6}} \cdot \frac{1}{x} u \cdot 2$

Step 10

Combine.

$\frac{28 \cdot 1}{v^{6} x} u \cdot 2$

Step 11

Multiply $28$ by $1$ .

$\frac{28}{v^{6} x} u \cdot 2$

Step 12

Combine $\frac{28}{v^{6} x}$ and $u$ .

$\frac{28 u}{v^{6} x} \cdot 2$

Step 13

Multiply $\frac{28 u}{v^{6} x} \cdot 2$ .

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Step 13.1

Combine $\frac{28 u}{v^{6} x}$ and $2$ .

$\frac{28 u \cdot 2}{v^{6} x}$

Step 13.2

Multiply $2$ by $28$ .

$\frac{56 u}{v^{6} x}$