Finite Math Examples

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

Step 1

Move $6^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Multiply $6$ by $6$ .

$\frac{a^{- 2} b}{36 a^{- 3} b^{- 2}}$

Step 3

Simplify.

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Step 3.1

Move $a^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{- 2} b a^{3}}{36 b^{- 2}}$

Step 3.2

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

$\frac{a^{- 2} b a^{3} b^{2}}{36}$

Step 4

Simplify the numerator.

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Step 4.1

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

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Step 4.1.1

Move $a^{3}$ .

$\frac{a^{3} a^{- 2} b \cdot b^{2}}{36}$

Step 4.1.2

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

$\frac{a^{3 - 2} b \cdot b^{2}}{36}$

Step 4.1.3

Subtract $2$ from $3$ .

$\frac{a^{1} b \cdot b^{2}}{36}$

Step 4.2

Simplify $a^{1} b$ .

$\frac{a b \cdot b^{2}}{36}$

Step 4.3

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

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Step 4.3.1

Move $b^{2}$ .

$\frac{a (b^{2} b)}{36}$

Step 4.3.2

Multiply $b^{2}$ by $b$ .

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Step 4.3.2.1

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

$\frac{a (b^{2} b^{1})}{36}$

Step 4.3.2.2

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

$\frac{a b^{2 + 1}}{36}$

Step 4.3.3

Add $2$ and $1$ .

$\frac{a b^{3}}{36}$