Basic Math Examples

${(\frac{- 3 c^{- 3}}{9 c^{2}})}^{- 1}$

Step 1

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

${(\frac{- 3}{9 c^{2} c^{3}})}^{- 1}$

Step 2

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

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Step 2.1

Move $c^{3}$ .

${(\frac{- 3}{9 (c^{3} c^{2})})}^{- 1}$

Step 2.2

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

${(\frac{- 3}{9 c^{3 + 2}})}^{- 1}$

Step 2.3

Add $3$ and $2$ .

${(\frac{- 3}{9 c^{5}})}^{- 1}$

Step 3

Cancel the common factor of $- 3$ and $9$ .

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Step 3.1

Factor $3$ out of $- 3$ .

${(\frac{3 (- 1)}{9 c^{5}})}^{- 1}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $9 c^{5}$ .

${(\frac{3 (- 1)}{3 (3 c^{5})})}^{- 1}$

Step 3.2.2

Cancel the common factor.

${(\frac{3 \cdot - 1}{3 (3 c^{5})})}^{- 1}$

Step 3.2.3

Rewrite the expression.

${(\frac{- 1}{3 c^{5}})}^{- 1}$

Step 4

Move the negative in front of the fraction.

${(- \frac{1}{3 c^{5}})}^{- 1}$

Step 5

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

$- 3 c^{5}$