Basic Math Examples

$(6 p^{- 7} v^{4}) (- 2 p^{2} v^{- 9})$

Step 1

Multiply $p^{- 7}$ by $p^{2}$ by adding the exponents.

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Step 1.1

Move $p^{2}$ .

$6 (p^{2} p^{- 7}) v^{4} (- 2 v^{- 9})$

Step 1.2

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

$6 p^{2 - 7} v^{4} (- 2 v^{- 9})$

Step 1.3

Subtract $7$ from $2$ .

$6 p^{- 5} v^{4} (- 2 v^{- 9})$

Step 2

Multiply $v^{4}$ by $v^{- 9}$ by adding the exponents.

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Step 2.1

Move $v^{- 9}$ .

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

Step 2.2

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

$6 p^{- 5} v^{- 9 + 4} \cdot - 2$

Step 2.3

Add $- 9$ and $4$ .

$6 p^{- 5} v^{- 5} \cdot - 2$

Step 3

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

$6 \frac{1}{p^{5}} v^{- 5} \cdot - 2$

Step 4

Combine $6$ and $\frac{1}{p^{5}}$ .

$\frac{6}{p^{5}} v^{- 5} \cdot - 2$

Step 5

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

$\frac{6}{p^{5}} \cdot \frac{1}{v^{5}} \cdot - 2$

Step 6

Combine.

$\frac{6 \cdot 1}{p^{5} v^{5}} \cdot - 2$

Step 7

Multiply $6$ by $1$ .

$\frac{6}{p^{5} v^{5}} \cdot - 2$

Step 8

Multiply $\frac{6}{p^{5} v^{5}} \cdot - 2$ .

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Step 8.1

Combine $\frac{6}{p^{5} v^{5}}$ and $- 2$ .

$\frac{6 \cdot - 2}{p^{5} v^{5}}$

Step 8.2

Multiply $6$ by $- 2$ .

$\frac{- 12}{p^{5} v^{5}}$

Step 9

Move the negative in front of the fraction.

$- \frac{12}{p^{5} v^{5}}$