Algebra Examples

$(- \frac{9}{4} a^{- 2} b^{7}) \cdot (- 16 a^{- 3} b^{- 6})$

Step 1

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

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Step 1.1

Move $a^{- 3}$ .

$- \frac{9}{4} \cdot (a^{- 3} a^{- 2} b^{7}) \cdot (- 16 b^{- 6})$

Step 1.2

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

$- \frac{9}{4} \cdot (a^{- 3 - 2} b^{7}) \cdot (- 16 b^{- 6})$

Step 1.3

Subtract $2$ from $- 3$ .

$- \frac{9}{4} \cdot (a^{- 5} b^{7}) \cdot (- 16 b^{- 6})$

Step 2

Multiply $b^{7}$ by $b^{- 6}$ by adding the exponents.

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Step 2.1

Move $b^{- 6}$ .

$- \frac{9}{4} \cdot (a^{- 5} (b^{- 6} b^{7})) \cdot - 16$

Step 2.2

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

$- \frac{9}{4} \cdot (a^{- 5} b^{- 6 + 7}) \cdot - 16$

Step 2.3

Add $- 6$ and $7$ .

$- \frac{9}{4} \cdot (a^{- 5} b^{1}) \cdot - 16$

Step 3

Simplify $- \frac{9}{4} \cdot (a^{- 5} b^{1}) \cdot - 16$ .

$- \frac{9}{4} \cdot (a^{- 5} b) \cdot - 16$

Step 4

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

$- \frac{9}{4} \cdot (\frac{1}{a^{5}} b) \cdot - 16$

Step 5

Combine $\frac{1}{a^{5}}$ and $b$ .

$- \frac{9}{4} \cdot \frac{b}{a^{5}} \cdot - 16$

Step 6

Multiply $\frac{b}{a^{5}}$ by $\frac{9}{4}$ .

$- \frac{b \cdot 9}{a^{5} \cdot 4} \cdot - 16$

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Move the leading negative in $- \frac{b \cdot 9}{a^{5} \cdot 4}$ into the numerator.

$\frac{- b \cdot 9}{a^{5} \cdot 4} \cdot - 16$

Step 7.2

Factor $4$ out of $a^{5} \cdot 4$ .

$\frac{- b \cdot 9}{4 \cdot a^{5}} \cdot - 16$

Step 7.3

Factor $4$ out of $- 16$ .

$\frac{- b \cdot 9}{4 \cdot a^{5}} \cdot (4 (- 4))$

Step 7.4

Cancel the common factor.

$\frac{- b \cdot 9}{4 \cdot a^{5}} \cdot (4 \cdot - 4)$

Step 7.5

Rewrite the expression.

$\frac{- b \cdot 9}{a^{5}} \cdot - 4$

Step 8

Multiply $9$ by $- 1$ .

$\frac{- 9 b}{a^{5}} \cdot - 4$

Step 9

Combine $\frac{- 9 b}{a^{5}}$ and $- 4$ .

$\frac{- 9 b \cdot - 4}{a^{5}}$

Step 10

Multiply $- 4$ by $- 9$ .

$\frac{36 b}{a^{5}}$