Finite Math Examples

$3 u^{3} v^{5} \cdot (2 w^{5} u) \cdot (7 w^{- 6} v^{8})$

Step 1

The polynomial cannot be factored using the grouping method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the grouping method.

Step 2

Remove unnecessary parentheses.

$3 u^{3} v^{5} \cdot 2 w^{5} u \cdot 7 w^{- 6} v^{8}$

Step 3

Combine exponents.

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Step 3.1

Multiply $2$ by $3$ .

$6 u^{3} v^{5} w^{5} u \cdot 7 w^{- 6} v^{8}$

Step 3.2

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

$6 (u^{1} u^{3}) v^{5} w^{5} \cdot 7 w^{- 6} v^{8}$

Step 3.3

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

$6 u^{1 + 3} v^{5} w^{5} \cdot 7 w^{- 6} v^{8}$

Step 3.4

Add $1$ and $3$ .

$6 u^{4} v^{5} w^{5} \cdot 7 w^{- 6} v^{8}$

Step 3.5

Multiply $7$ by $6$ .

$42 u^{4} v^{5} w^{5} w^{- 6} v^{8}$

Step 3.6

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

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Step 3.6.1

Move $w^{- 6}$ .

$42 u^{4} v^{5} (w^{- 6} w^{5}) v^{8}$

Step 3.6.2

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

$42 u^{4} v^{5} w^{- 6 + 5} v^{8}$

Step 3.6.3

Add $- 6$ and $5$ .

$42 u^{4} v^{5} w^{- 1} v^{8}$

Step 3.7

Multiply $v^{5}$ by $v^{8}$ by adding the exponents.

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Step 3.7.1

Move $v^{8}$ .

$42 u^{4} (v^{8} v^{5}) w^{- 1}$

Step 3.7.2

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

$42 u^{4} v^{8 + 5} w^{- 1}$

Step 3.7.3

Add $8$ and $5$ .

$42 u^{4} v^{13} w^{- 1}$