Finite Math Examples

$(36 m^{8} - 42 m^{5} - 9 m^{2}) {(3 m^{4})}^{- 1}$

Step 1

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

$(36 m^{8} - 42 m^{5} - 9 m^{2}) \frac{1}{3 m^{4}}$

Step 2

Multiply $36 m^{8} - 42 m^{5} - 9 m^{2}$ by $\frac{1}{3 m^{4}}$ .

$\frac{36 m^{8} - 42 m^{5} - 9 m^{2}}{3 m^{4}}$

Step 3

Factor $3 m^{2}$ out of $36 m^{8} - 42 m^{5} - 9 m^{2}$ .

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Step 3.1

Factor $3 m^{2}$ out of $36 m^{8}$ .

$\frac{3 m^{2} (12 m^{6}) - 42 m^{5} - 9 m^{2}}{3 m^{4}}$

Step 3.2

Factor $3 m^{2}$ out of $- 42 m^{5}$ .

$\frac{3 m^{2} (12 m^{6}) + 3 m^{2} (- 14 m^{3}) - 9 m^{2}}{3 m^{4}}$

Step 3.3

Factor $3 m^{2}$ out of $- 9 m^{2}$ .

$\frac{3 m^{2} (12 m^{6}) + 3 m^{2} (- 14 m^{3}) + 3 m^{2} (- 3)}{3 m^{4}}$

Step 3.4

Factor $3 m^{2}$ out of $3 m^{2} (12 m^{6}) + 3 m^{2} (- 14 m^{3})$ .

$\frac{3 m^{2} (12 m^{6} - 14 m^{3}) + 3 m^{2} (- 3)}{3 m^{4}}$

Step 3.5

Factor $3 m^{2}$ out of $3 m^{2} (12 m^{6} - 14 m^{3}) + 3 m^{2} (- 3)$ .

$\frac{3 m^{2} (12 m^{6} - 14 m^{3} - 3)}{3 m^{4}}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$\frac{3 m^{2} (12 m^{6} - 14 m^{3} - 3)}{3 m^{4}}$

Step 4.2

Rewrite the expression.

$\frac{m^{2} (12 m^{6} - 14 m^{3} - 3)}{m^{4}}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $m^{2}$ out of $m^{4}$ .

$\frac{m^{2} (12 m^{6} - 14 m^{3} - 3)}{m^{2} m^{2}}$

Step 5.2

Cancel the common factor.

$\frac{m^{2} (12 m^{6} - 14 m^{3} - 3)}{m^{2} m^{2}}$

Step 5.3

Rewrite the expression.

$\frac{12 m^{6} - 14 m^{3} - 3}{m^{2}}$