Basic Math Examples

$2 v n^{- 4} \cdot (2 w n^{5} v^{9}) \cdot (5 w^{- 6})$

Step 1

Multiply $v$ by $v^{9}$ by adding the exponents.

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Step 1.1

Move $v^{9}$ .

$2 (v^{9} v) n^{- 4} \cdot (2 w n^{5}) \cdot (5 w^{- 6})$

Step 1.2

Multiply $v^{9}$ by $v$ .

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Step 1.2.1

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

$2 (v^{9} v^{1}) n^{- 4} \cdot (2 w n^{5}) \cdot (5 w^{- 6})$

Step 1.2.2

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

$2 v^{9 + 1} n^{- 4} \cdot (2 w n^{5}) \cdot (5 w^{- 6})$

Step 1.3

Add $9$ and $1$ .

$2 v^{10} n^{- 4} \cdot (2 w n^{5}) \cdot (5 w^{- 6})$

Step 2

Multiply $n^{- 4}$ by $n^{5}$ by adding the exponents.

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Step 2.1

Move $n^{5}$ .

$2 v^{10} (n^{5} n^{- 4}) \cdot (2 w) \cdot (5 w^{- 6})$

Step 2.2

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

$2 v^{10} n^{5 - 4} \cdot (2 w) \cdot (5 w^{- 6})$

Step 2.3

Subtract $4$ from $5$ .

$2 v^{10} n^{1} \cdot (2 w) \cdot (5 w^{- 6})$

Step 3

Simplify $2 v^{10} n^{1} \cdot (2 w) \cdot (5 w^{- 6})$ .

$2 v^{10} n \cdot (2 w) \cdot (5 w^{- 6})$

Step 4

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

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Step 4.1

Move $w^{- 6}$ .

$2 v^{10} n \cdot (2 (w^{- 6} w)) \cdot 5$

Step 4.2

Multiply $w^{- 6}$ by $w$ .

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Step 4.2.1

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

$2 v^{10} n \cdot (2 (w^{- 6} w^{1})) \cdot 5$

Step 4.2.2

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

$2 v^{10} n \cdot (2 w^{- 6 + 1}) \cdot 5$

Step 4.3

Add $- 6$ and $1$ .

$2 v^{10} n \cdot (2 w^{- 5}) \cdot 5$

Step 5

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

$2 v^{10} n \cdot (2 \frac{1}{w^{5}}) \cdot 5$

Step 6

Combine $2$ and $\frac{1}{w^{5}}$ .

$2 v^{10} n \cdot \frac{2}{w^{5}} \cdot 5$

Step 7

Multiply $2 v^{10} n \frac{2}{w^{5}}$ .

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Step 7.1

Combine $2$ and $\frac{2}{w^{5}}$ .

$v^{10} n \frac{2 \cdot 2}{w^{5}} \cdot 5$

Step 7.2

Multiply $2$ by $2$ .

$v^{10} n \frac{4}{w^{5}} \cdot 5$

Step 7.3

Combine $v^{10}$ and $\frac{4}{w^{5}}$ .

$n \frac{v^{10} \cdot 4}{w^{5}} \cdot 5$

Step 7.4

Combine $n$ and $\frac{v^{10} \cdot 4}{w^{5}}$ .

$\frac{n (v^{10} \cdot 4)}{w^{5}} \cdot 5$

Step 8

Move $4$ to the left of $n v^{10}$ .

$\frac{4 \cdot (n v^{10})}{w^{5}} \cdot 5$

Step 9

Multiply $\frac{4 n v^{10}}{w^{5}} \cdot 5$ .

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Step 9.1

Combine $\frac{4 n v^{10}}{w^{5}}$ and $5$ .

$\frac{4 n v^{10} \cdot 5}{w^{5}}$

Step 9.2

Multiply $5$ by $4$ .

$\frac{20 n v^{10}}{w^{5}}$