Finite Math Examples

$\frac{3 m^{- 2} n^{- 4} p^{- 1}}{9 m n^{- 6} p^{- 3}}$

Step 1

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

$\frac{3 n^{- 4} p^{- 1}}{9 m n^{- 6} p^{- 3} m^{2}}$

Step 2

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

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Step 2.1

Move $m^{2}$ .

$\frac{3 n^{- 4} p^{- 1}}{9 (m^{2} m) n^{- 6} p^{- 3}}$

Step 2.2

Multiply $m^{2}$ by $m$ .

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Step 2.2.1

Raise $m$ to the power of $1$ .

$\frac{3 n^{- 4} p^{- 1}}{9 (m^{2} m^{1}) n^{- 6} p^{- 3}}$

Step 2.2.2

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

$\frac{3 n^{- 4} p^{- 1}}{9 m^{2 + 1} n^{- 6} p^{- 3}}$

Step 2.3

Add $2$ and $1$ .

$\frac{3 n^{- 4} p^{- 1}}{9 m^{3} n^{- 6} p^{- 3}}$

Step 3

Move $n^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 n^{- 4} p^{- 1} n^{6}}{9 m^{3} p^{- 3}}$

Step 4

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

$\frac{3 n^{- 4} p^{- 1} n^{6} p^{3}}{9 m^{3}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $n^{- 4}$ by $n^{6}$ by adding the exponents.

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Step 5.1.1

Move $n^{6}$ .

$\frac{3 (n^{6} n^{- 4}) p^{- 1} p^{3}}{9 m^{3}}$

Step 5.1.2

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

$\frac{3 n^{6 - 4} p^{- 1} p^{3}}{9 m^{3}}$

Step 5.1.3

Subtract $4$ from $6$ .

$\frac{3 n^{2} p^{- 1} p^{3}}{9 m^{3}}$

Step 5.2

Multiply $p^{- 1}$ by $p^{3}$ by adding the exponents.

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Step 5.2.1

Move $p^{3}$ .

$\frac{3 n^{2} (p^{3} p^{- 1})}{9 m^{3}}$

Step 5.2.2

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

$\frac{3 n^{2} p^{3 - 1}}{9 m^{3}}$

Step 5.2.3

Subtract $1$ from $3$ .

$\frac{3 n^{2} p^{2}}{9 m^{3}}$

Step 6

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

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Step 6.1

Factor $3$ out of $3 n^{2} p^{2}$ .

$\frac{3 (n^{2} p^{2})}{9 m^{3}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{3 (n^{2} p^{2})}{3 (3 m^{3})}$

Step 6.2.2

Cancel the common factor.

$\frac{3 (n^{2} p^{2})}{3 (3 m^{3})}$

Step 6.2.3

Rewrite the expression.

$\frac{n^{2} p^{2}}{3 m^{3}}$