Finite Math Examples

$3 u^{6} w^{- 1} \cdot (3 u^{6} x^{9}) \cdot (7 x^{- 7} w)$

Step 1

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

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Step 1.1

Move $u^{6}$ .

$3 (u^{6} u^{6}) w^{- 1} \cdot (3 x^{9}) \cdot (7 x^{- 7} w)$

Step 1.2

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

$3 u^{6 + 6} w^{- 1} \cdot (3 x^{9}) \cdot (7 x^{- 7} w)$

Step 1.3

Add $6$ and $6$ .

$3 u^{12} w^{- 1} \cdot (3 x^{9}) \cdot (7 x^{- 7} w)$

Step 2

Multiply $w^{- 1}$ by $w$ by adding the exponents.

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Step 2.1

Move $w$ .

$3 u^{12} (w \cdot w^{- 1}) \cdot (3 x^{9}) \cdot (7 x^{- 7})$

Step 2.2

Multiply $w$ by $w^{- 1}$ .

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Step 2.2.1

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

$3 u^{12} (w^{1} w^{- 1}) \cdot (3 x^{9}) \cdot (7 x^{- 7})$

Step 2.2.2

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

$3 u^{12} w^{1 - 1} \cdot (3 x^{9}) \cdot (7 x^{- 7})$

Step 2.3

Subtract $1$ from $1$ .

$3 u^{12} w^{0} \cdot (3 x^{9}) \cdot (7 x^{- 7})$

Step 3

Simplify $3 u^{12} w^{0} \cdot (3 x^{9}) \cdot (7 x^{- 7})$ .

$3 u^{12} \cdot (3 x^{9}) \cdot (7 x^{- 7})$

Step 4

Multiply $x^{9}$ by $x^{- 7}$ by adding the exponents.

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Step 4.1

Move $x^{- 7}$ .

$3 u^{12} \cdot (3 (x^{- 7} x^{9})) \cdot 7$

Step 4.2

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

$3 u^{12} \cdot (3 x^{- 7 + 9}) \cdot 7$

Step 4.3

Add $- 7$ and $9$ .

$3 u^{12} \cdot (3 x^{2}) \cdot 7$

Step 5

Rewrite using the commutative property of multiplication.

$3 \cdot 3 u^{12} x^{2} \cdot 7$

Step 6

Multiply $3$ by $3$ .

$9 u^{12} x^{2} \cdot 7$

Step 7

Multiply $7$ by $9$ .

$63 u^{12} x^{2}$