Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the numerator.

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Step 3.1

Multiply $m^{9}$ by $m^{3}$ by adding the exponents.

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Step 3.1.1

Move $m^{3}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Add $3$ and $9$ .

$\frac{2 m^{12} n^{4} n^{2}}{- 4}$

Step 3.2

Multiply $n^{4}$ by $n^{2}$ by adding the exponents.

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Step 3.2.1

Move $n^{2}$ .

$\frac{2 m^{12} (n^{2} n^{4})}{- 4}$

Step 3.2.2

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

$\frac{2 m^{12} n^{2 + 4}}{- 4}$

Step 3.2.3

Add $2$ and $4$ .

$\frac{2 m^{12} n^{6}}{- 4}$

Step 4

Cancel the common factor of $2$ and $- 4$ .

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Step 4.1

Factor $2$ out of $2 m^{12} n^{6}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $- 4$ .

$\frac{2 (m^{12} n^{6})}{2 \cdot - 2}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (m^{12} n^{6})}{2 \cdot - 2}$

Step 4.2.3

Rewrite the expression.

$\frac{m^{12} n^{6}}{- 2}$

Step 5

Move the negative in front of the fraction.

$- \frac{m^{12} n^{6}}{2}$