Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify the denominator.

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Step 4.1

Multiply $a$ by $a$ by adding the exponents.

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Step 4.1.1

Move $a$ .

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

Step 4.1.2

Multiply $a$ by $a$ .

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

Step 4.2

Multiply $b^{- 1}$ by $b^{2}$ by adding the exponents.

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Step 4.2.1

Move $b^{2}$ .

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

Step 4.2.2

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

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

Step 4.2.3

Subtract $1$ from $2$ .

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

Step 4.3

Simplify $2 a^{2} b^{1} \cdot 3$ .

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

Step 5

Multiply $3$ by $2$ .

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

Step 6

Change the sign of the exponent by rewriting the base as its reciprocal.

$6 a^{2} b$