Finite Math Examples

$\frac{- 15 m^{5} n^{- 7}}{3 m^{- 2} n^{- 3}}$

Step 1

Move $n^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 15 m^{5}}{3 m^{- 2} n^{- 3} n^{7}}$

Step 2

Multiply $n^{- 3}$ by $n^{7}$ by adding the exponents.

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Step 2.1

Move $n^{7}$ .

$\frac{- 15 m^{5}}{3 m^{- 2} (n^{7} n^{- 3})}$

Step 2.2

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

$\frac{- 15 m^{5}}{3 m^{- 2} n^{7 - 3}}$

Step 2.3

Subtract $3$ from $7$ .

$\frac{- 15 m^{5}}{3 m^{- 2} n^{4}}$

Step 3

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

$\frac{- 15 m^{5} m^{2}}{3 n^{4}}$

Step 4

Multiply $m^{5}$ by $m^{2}$ by adding the exponents.

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Step 4.1

Move $m^{2}$ .

$\frac{- 15 (m^{2} m^{5})}{3 n^{4}}$

Step 4.2

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

$\frac{- 15 m^{2 + 5}}{3 n^{4}}$

Step 4.3

Add $2$ and $5$ .

$\frac{- 15 m^{7}}{3 n^{4}}$

Step 5

Cancel the common factor of $- 15$ and $3$ .

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Step 5.1

Factor $3$ out of $- 15 m^{7}$ .

$\frac{3 (- 5 m^{7})}{3 n^{4}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $3 n^{4}$ .

$\frac{3 (- 5 m^{7})}{3 (n^{4})}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (- 5 m^{7})}{3 n^{4}}$

Step 5.2.3

Rewrite the expression.

$\frac{- 5 m^{7}}{n^{4}}$

Step 6

Move the negative in front of the fraction.

$- \frac{5 m^{7}}{n^{4}}$