Algebra Examples

$\frac{20 {(m n)}^{- 3}}{- 5 m^{2} n^{2}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

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

$\frac{20}{- 5 m^{2} n^{2} {(m n)}^{3}}$

Step 1.2

Cancel the common factor of $20$ and $- 5$ .

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Step 1.2.1

Factor $5$ out of $20$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $m n$ .

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

Step 2.2

Combine exponents.

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Step 2.2.1

Multiply $m^{2}$ by $m^{3}$ by adding the exponents.

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Step 2.2.1.1

Move $m^{3}$ .

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

Step 2.2.1.2

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

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

Step 2.2.1.3

Add $3$ and $2$ .

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

Step 2.2.2

Multiply $n^{2}$ by $n^{3}$ by adding the exponents.

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Step 2.2.2.1

Move $n^{3}$ .

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

Step 2.2.2.2

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

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

Step 2.2.2.3

Add $3$ and $2$ .

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

Step 3

Move the negative in front of the fraction.

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