Algebra Examples

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

Step 1

Combine.

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

Step 2

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

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Step 2.1

Move $a$ .

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

Step 2.2

Multiply $a$ by $a^{3}$ .

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Step 2.2.1

Raise $a$ to the power of $1$ .

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

Step 2.2.2

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

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

Step 2.3

Add $1$ and $3$ .

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

Step 3

Move $b^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 4

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

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Step 4.1

Move $b^{2}$ .

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

Step 4.2

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

$\frac{a^{4} b^{2 + 2}}{a^{4}}$

Step 4.3

Add $2$ and $2$ .

$\frac{a^{4} b^{4}}{a^{4}}$

Step 5

Cancel the common factor of $a^{4}$ .

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Step 5.1

Cancel the common factor.

$\frac{a^{4} b^{4}}{a^{4}}$

Step 5.2

Divide $b^{4}$ by $1$ .

$b^{4}$