Basic Math Examples

$(\frac{4 a^{4} b^{3}}{a^{5} b^{6}}) (\frac{- a^{3}}{- (b^{2})})$

Step 1

Combine.

$\frac{4 a^{4} b^{3} (- a^{3})}{a^{5} b^{6} (- (b^{2}))}$

Step 2

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

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Step 2.1

Move $a^{3}$ .

$\frac{4 (a^{3} a^{4}) b^{3} \cdot - 1}{a^{5} b^{6} (- (b^{2}))}$

Step 2.2

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

$\frac{4 a^{3 + 4} b^{3} \cdot - 1}{a^{5} b^{6} (- (b^{2}))}$

Step 2.3

Add $3$ and $4$ .

$\frac{4 a^{7} b^{3} \cdot - 1}{a^{5} b^{6} (- (b^{2}))}$

Step 3

Multiply $b^{6}$ by $b^{2}$ by adding the exponents.

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Step 3.1

Move $b^{2}$ .

$\frac{4 a^{7} b^{3} \cdot - 1}{a^{5} (b^{2} b^{6}) \cdot - 1}$

Step 3.2

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

$\frac{4 a^{7} b^{3} \cdot - 1}{a^{5} b^{2 + 6} \cdot - 1}$

Step 3.3

Add $2$ and $6$ .

$\frac{4 a^{7} b^{3} \cdot - 1}{a^{5} b^{8} \cdot - 1}$

Step 4

Cancel the common factor of $a^{7}$ and $a^{5}$ .

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Step 4.1

Factor $a^{5}$ out of $4 a^{7} b^{3} \cdot - 1$ .

$\frac{a^{5} (4 a^{2} b^{3} \cdot - 1)}{a^{5} b^{8} \cdot - 1}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{5}$ out of $a^{5} b^{8} \cdot - 1$ .

$\frac{a^{5} (4 a^{2} b^{3} \cdot - 1)}{a^{5} (b^{8} \cdot - 1)}$

Step 4.2.2

Cancel the common factor.

$\frac{a^{5} (4 a^{2} b^{3} \cdot - 1)}{a^{5} (b^{8} \cdot - 1)}$

Step 4.2.3

Rewrite the expression.

$\frac{4 a^{2} b^{3} \cdot - 1}{b^{8} \cdot - 1}$

Step 5

Cancel the common factor of $b^{3}$ and $b^{8}$ .

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Step 5.1

Factor $b^{3}$ out of $4 a^{2} b^{3} \cdot - 1$ .

$\frac{b^{3} (4 a^{2} \cdot - 1)}{b^{8} \cdot - 1}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $b^{3}$ out of $b^{8} \cdot - 1$ .

$\frac{b^{3} (4 a^{2} \cdot - 1)}{b^{3} (b^{5} \cdot - 1)}$

Step 5.2.2

Cancel the common factor.

$\frac{b^{3} (4 a^{2} \cdot - 1)}{b^{3} (b^{5} \cdot - 1)}$

Step 5.2.3

Rewrite the expression.

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

Step 6

Dividing two negative values results in a positive value.

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