Algebra Examples

${(\frac{9 m^{4} n^{10}}{- 3 m^{2} n^{5}})}^{- 1}$

Step 1

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

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Step 1.1

Factor $3$ out of $9 m^{4} n^{10}$ .

${(\frac{3 (3 m^{4} n^{10})}{- 3 m^{2} n^{5}})}^{- 1}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $- 3 m^{2} n^{5}$ .

${(\frac{3 (3 m^{4} n^{10})}{3 (- m^{2} n^{5})})}^{- 1}$

Step 1.2.2

Cancel the common factor.

${(\frac{3 (3 m^{4} n^{10})}{3 (- m^{2} n^{5})})}^{- 1}$

Step 1.2.3

Rewrite the expression.

${(\frac{3 m^{4} n^{10}}{- m^{2} n^{5}})}^{- 1}$

Step 2

Cancel the common factor of $m^{4}$ and $m^{2}$ .

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Step 2.1

Factor $m^{2}$ out of $3 m^{4} n^{10}$ .

${(\frac{m^{2} (3 m^{2} n^{10})}{- m^{2} n^{5}})}^{- 1}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $m^{2}$ out of $- m^{2} n^{5}$ .

${(\frac{m^{2} (3 m^{2} n^{10})}{m^{2} (- 1 n^{5})})}^{- 1}$

Step 2.2.2

Cancel the common factor.

${(\frac{m^{2} (3 m^{2} n^{10})}{m^{2} (- 1 n^{5})})}^{- 1}$

Step 2.2.3

Rewrite the expression.

${(\frac{3 m^{2} n^{10}}{- 1 n^{5}})}^{- 1}$

Step 3

Cancel the common factor of $n^{10}$ and $n^{5}$ .

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Step 3.1

Factor $n^{5}$ out of $3 m^{2} n^{10}$ .

${(\frac{n^{5} (3 m^{2} n^{5})}{- 1 n^{5}})}^{- 1}$

Step 3.2

Move the negative one from the denominator of $\frac{3 m^{2} n^{5}}{- 1}$ .

${(- 1 \cdot (3 m^{2} n^{5}))}^{- 1}$

Step 4

Simplify the expression.

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Step 4.1

Rewrite $- 1 \cdot (3 m^{2} n^{5})$ as $- (3 m^{2} n^{5})$ .

${(- (3 m^{2} n^{5}))}^{- 1}$

Step 4.2

Multiply $3$ by $- 1$ .

${(- 3 (m^{2} n^{5}))}^{- 1}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{- 3 m^{2} n^{5}}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{3 m^{2} n^{5}}$