Finite Math Examples

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

Step 1

Multiply $u^{- 6}$ by $u^{9}$ by adding the exponents.

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Step 1.1

Move $u^{9}$ .

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

Step 1.2

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

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

Step 1.3

Subtract $6$ from $9$ .

$6 u^{3} v^{- 8} \cdot (8 w^{6}) \cdot (2 v w^{- 7})$

Step 2

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

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Step 2.1

Move $v$ .

$6 u^{3} (v \cdot v^{- 8}) \cdot (8 w^{6}) \cdot (2 w^{- 7})$

Step 2.2

Multiply $v$ by $v^{- 8}$ .

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Step 2.2.1

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

$6 u^{3} (v^{1} v^{- 8}) \cdot (8 w^{6}) \cdot (2 w^{- 7})$

Step 2.2.2

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

$6 u^{3} v^{1 - 8} \cdot (8 w^{6}) \cdot (2 w^{- 7})$

Step 2.3

Subtract $8$ from $1$ .

$6 u^{3} v^{- 7} \cdot (8 w^{6}) \cdot (2 w^{- 7})$

Step 3

Multiply $w^{6}$ by $w^{- 7}$ by adding the exponents.

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Step 3.1

Move $w^{- 7}$ .

$6 u^{3} v^{- 7} \cdot (8 (w^{- 7} w^{6})) \cdot 2$

Step 3.2

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

$6 u^{3} v^{- 7} \cdot (8 w^{- 7 + 6}) \cdot 2$

Step 3.3

Add $- 7$ and $6$ .

$6 u^{3} v^{- 7} \cdot (8 w^{- 1}) \cdot 2$

Step 4

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

$6 u^{3} \frac{1}{v^{7}} \cdot (8 w^{- 1}) \cdot 2$

Step 5

Multiply $6 u^{3} \frac{1}{v^{7}}$ .

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Step 5.1

Combine $6$ and $\frac{1}{v^{7}}$ .

$u^{3} \frac{6}{v^{7}} \cdot (8 w^{- 1}) \cdot 2$

Step 5.2

Combine $u^{3}$ and $\frac{6}{v^{7}}$ .

$\frac{u^{3} \cdot 6}{v^{7}} \cdot (8 w^{- 1}) \cdot 2$

Step 6

Rewrite using the commutative property of multiplication.

$8 \frac{u^{3} \cdot 6}{v^{7}} w^{- 1} \cdot 2$

Step 7

Move $6$ to the left of $u^{3}$ .

$8 \frac{6 \cdot u^{3}}{v^{7}} w^{- 1} \cdot 2$

Step 8

Multiply $8 \frac{6 u^{3}}{v^{7}}$ .

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Step 8.1

Combine $8$ and $\frac{6 u^{3}}{v^{7}}$ .

$\frac{8 (6 u^{3})}{v^{7}} w^{- 1} \cdot 2$

Step 8.2

Multiply $6$ by $8$ .

$\frac{48 u^{3}}{v^{7}} w^{- 1} \cdot 2$

Step 9

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

$\frac{48 u^{3}}{v^{7}} \cdot \frac{1}{w} \cdot 2$

Step 10

Combine.

$\frac{48 u^{3} \cdot 1}{v^{7} w} \cdot 2$

Step 11

Multiply $48$ by $1$ .

$\frac{48 u^{3}}{v^{7} w} \cdot 2$

Step 12

Multiply $\frac{48 u^{3}}{v^{7} w} \cdot 2$ .

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Step 12.1

Combine $\frac{48 u^{3}}{v^{7} w}$ and $2$ .

$\frac{48 u^{3} \cdot 2}{v^{7} w}$

Step 12.2

Multiply $2$ by $48$ .

$\frac{96 u^{3}}{v^{7} w}$