Algebra Examples

$- 2 p^{4} q^{- 2} \cdot 3 p^{- 3} q^{- 4}$

Step 1

Multiply $p^{4}$ by $p^{- 3}$ by adding the exponents.

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Step 1.1

Move $p^{- 3}$ .

$- 2 (p^{- 3} p^{4}) q^{- 2} \cdot (3 q^{- 4})$

Step 1.2

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

$- 2 p^{- 3 + 4} q^{- 2} \cdot (3 q^{- 4})$

Step 1.3

Add $- 3$ and $4$ .

$- 2 p^{1} q^{- 2} \cdot (3 q^{- 4})$

Step 2

Simplify $- 2 p^{1} q^{- 2} \cdot (3 q^{- 4})$ .

$- 2 p q^{- 2} \cdot (3 q^{- 4})$

Step 3

Multiply $q^{- 2}$ by $q^{- 4}$ by adding the exponents.

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Step 3.1

Move $q^{- 4}$ .

$- 2 p (q^{- 4} q^{- 2}) \cdot 3$

Step 3.2

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

$- 2 p q^{- 4 - 2} \cdot 3$

Step 3.3

Subtract $2$ from $- 4$ .

$- 2 p q^{- 6} \cdot 3$

Step 4

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

$- 2 p \frac{1}{q^{6}} \cdot 3$

Step 5

Multiply $- 2 p \frac{1}{q^{6}}$ .

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Step 5.1

Combine $- 2$ and $\frac{1}{q^{6}}$ .

$p \frac{- 2}{q^{6}} \cdot 3$

Step 5.2

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

$\frac{p \cdot - 2}{q^{6}} \cdot 3$

Step 6

Move $- 2$ to the left of $p$ .

$\frac{- 2 \cdot p}{q^{6}} \cdot 3$

Step 7

Move the negative in front of the fraction.

$- \frac{2 \cdot p}{q^{6}} \cdot 3$

Step 8

Multiply $- \frac{2 p}{q^{6}} \cdot 3$ .

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Step 8.1

Multiply $3$ by $- 1$ .

$- 3 \frac{2 p}{q^{6}}$

Step 8.2

Combine $- 3$ and $\frac{2 p}{q^{6}}$ .

$\frac{- 3 (2 p)}{q^{6}}$

Step 8.3

Multiply $2$ by $- 3$ .

$\frac{- 6 p}{q^{6}}$

Step 9

Move the negative in front of the fraction.

$- \frac{6 p}{q^{6}}$