Algebra Examples

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

Step 1

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

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Step 1.1

Move $a^{- 4}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 4$ and $3$ .

$4 a^{- 1} b^{2} \cdot (3 b^{- 3})$

Step 2

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

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Step 2.1

Move $b^{- 3}$ .

$4 a^{- 1} (b^{- 3} b^{2}) \cdot 3$

Step 2.2

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

$4 a^{- 1} b^{- 3 + 2} \cdot 3$

Step 2.3

Add $- 3$ and $2$ .

$4 a^{- 1} b^{- 1} \cdot 3$

Step 3

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

$4 \frac{1}{a} b^{- 1} \cdot 3$

Step 4

Combine $4$ and $\frac{1}{a}$ .

$\frac{4}{a} b^{- 1} \cdot 3$

Step 5

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

$\frac{4}{a} \cdot \frac{1}{b} \cdot 3$

Step 6

Multiply $\frac{4}{a}$ by $\frac{1}{b}$ .

$\frac{4}{a b} \cdot 3$

Step 7

Multiply $\frac{4}{a b} \cdot 3$ .

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Step 7.1

Combine $\frac{4}{a b}$ and $3$ .

$\frac{4 \cdot 3}{a b}$

Step 7.2

Multiply $4$ by $3$ .

$\frac{12}{a b}$