Precalculus Examples

$(- 4 a^{2} b^{- 5}) (2 a^{3} b^{4})$

Step 1

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

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Step 1.1

Move $a^{3}$ .

$- 4 (a^{3} a^{2}) b^{- 5} (2 b^{4})$

Step 1.2

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

$- 4 a^{3 + 2} b^{- 5} (2 b^{4})$

Step 1.3

Add $3$ and $2$ .

$- 4 a^{5} b^{- 5} (2 b^{4})$

Step 2

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

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Step 2.1

Move $b^{4}$ .

$- 4 a^{5} (b^{4} b^{- 5}) \cdot 2$

Step 2.2

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

$- 4 a^{5} b^{4 - 5} \cdot 2$

Step 2.3

Subtract $5$ from $4$ .

$- 4 a^{5} b^{- 1} \cdot 2$

Step 3

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

$- 4 a^{5} \frac{1}{b} \cdot 2$

Step 4

Multiply $- 4 a^{5} \frac{1}{b}$ .

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Step 4.1

Combine $- 4$ and $\frac{1}{b}$ .

$a^{5} \frac{- 4}{b} \cdot 2$

Step 4.2

Combine $a^{5}$ and $\frac{- 4}{b}$ .

$\frac{a^{5} \cdot - 4}{b} \cdot 2$

Step 5

Move $- 4$ to the left of $a^{5}$ .

$\frac{- 4 \cdot a^{5}}{b} \cdot 2$

Step 6

Move the negative in front of the fraction.

$- \frac{4 \cdot a^{5}}{b} \cdot 2$

Step 7

Multiply $- \frac{4 a^{5}}{b} \cdot 2$ .

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Step 7.1

Multiply $2$ by $- 1$ .

$- 2 \frac{4 a^{5}}{b}$

Step 7.2

Combine $- 2$ and $\frac{4 a^{5}}{b}$ .

$\frac{- 2 (4 a^{5})}{b}$

Step 7.3

Multiply $4$ by $- 2$ .

$\frac{- 8 a^{5}}{b}$

Step 8

Move the negative in front of the fraction.

$- \frac{8 a^{5}}{b}$