Basic Math Examples

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

Step 1

Move $a^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

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Step 2.1

Move $a^{4}$ .

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

Step 2.2

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

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

Step 2.3

Subtract $2$ from $4$ .

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

Step 3

Cancel the common factor of $8$ and $4$ .

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Step 3.1

Factor $4$ out of $8 b^{3}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $4 a^{2} \cdot (4 b^{2})$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $2$ and $4$ .

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Step 4.1

Factor $2$ out of $2 b^{3}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $a^{2} \cdot (4 b^{2})$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $b^{3}$ and $b^{2}$ .

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Step 5.1

Factor $b^{2}$ out of $b^{3}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $b^{2}$ out of $a^{2} \cdot (2 b^{2})$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Move $2$ to the left of $a^{2}$ .

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