Algebra Examples

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

Step 1

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

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Step 1.1

Move $b^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add $2$ and $4$ .

$\frac{- 3 a^{2} b^{6}}{- 2 a^{2} b^{- 1}}$

Step 2

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

$\frac{- 3 a^{2} b^{6} b}{- 2 a^{2}}$

Step 3

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

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Step 3.1

Move $b$ .

$\frac{- 3 a^{2} (b \cdot b^{6})}{- 2 a^{2}}$

Step 3.2

Multiply $b$ by $b^{6}$ .

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Step 3.2.1

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

$\frac{- 3 a^{2} (b^{1} b^{6})}{- 2 a^{2}}$

Step 3.2.2

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

$\frac{- 3 a^{2} b^{1 + 6}}{- 2 a^{2}}$

Step 3.3

Add $1$ and $6$ .

$\frac{- 3 a^{2} b^{7}}{- 2 a^{2}}$

Step 4

Cancel the common factor of $a^{2}$ .

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Step 4.1

Cancel the common factor.

$\frac{- 3 a^{2} b^{7}}{- 2 a^{2}}$

Step 4.2

Rewrite the expression.

$\frac{- 3 b^{7}}{- 2}$

Step 5

Dividing two negative values results in a positive value.

$\frac{3 b^{7}}{2}$