Trigonometry Examples

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

Step 1

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

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Step 1.1

Move $u^{5}$ .

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

Step 1.2

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

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

Step 1.3

Subtract $5$ from $5$ .

$3 u^{0} x^{7} \cdot (2 x^{- 7} w) \cdot (7 w^{8})$

Step 2

Simplify $3 u^{0} x^{7} \cdot (2 x^{- 7} w) \cdot (7 w^{8})$ .

$3 x^{7} \cdot (2 x^{- 7} w) \cdot (7 w^{8})$

Step 3

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

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Step 3.1

Move $x^{- 7}$ .

$3 (x^{- 7} x^{7}) \cdot (2 w) \cdot (7 w^{8})$

Step 3.2

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

$3 x^{- 7 + 7} \cdot (2 w) \cdot (7 w^{8})$

Step 3.3

Add $- 7$ and $7$ .

$3 x^{0} \cdot (2 w) \cdot (7 w^{8})$

Step 4

Simplify $3 x^{0} \cdot (2 w) \cdot (7 w^{8})$ .

$3 \cdot (2 w) \cdot (7 w^{8})$

Step 5

Multiply $w$ by $w^{8}$ by adding the exponents.

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Step 5.1

Move $w^{8}$ .

$3 \cdot (2 (w^{8} w)) \cdot 7$

Step 5.2

Multiply $w^{8}$ by $w$ .

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Step 5.2.1

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

$3 \cdot (2 (w^{8} w^{1})) \cdot 7$

Step 5.2.2

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

$3 \cdot (2 w^{8 + 1}) \cdot 7$

Step 5.3

Add $8$ and $1$ .

$3 \cdot (2 w^{9}) \cdot 7$

Step 6

Multiply $2$ by $3$ .

$6 w^{9} \cdot 7$

Step 7

Multiply $7$ by $6$ .

$42 w^{9}$