Basic Math Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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Step 2.1.1

Move $b^{2}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Subtract $1$ from $2$ .

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

Step 2.2

Simplify $2 a b^{1}$ .

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

Step 3

Cancel the common factor of $6$ and $2$ .

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Step 3.1

Factor $2$ out of $6 a^{2}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 a b$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a$ out of $a b$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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

Step 6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 6.1

Apply the product rule to $\frac{b}{3 a}$ .

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

Step 6.2

Apply the product rule to $3 a$ .

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

Step 7

Raise $3$ to the power of $2$ .

$\frac{b^{2}}{9 a^{2}}$