Algebra Examples

$\frac{m^{- 2} n^{- 5}}{{(m^{4} n^{3})}^{- 1}}$

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{n^{- 5}}{{(m^{4} n^{3})}^{- 1} m^{2}}$

Step 1.2

Move $n^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(m^{4} n^{3})}^{- 1} m^{2} n^{5}}$

Step 1.3

Move ${(m^{4} n^{3})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Cancel the common factor of $m^{4}$ and $m^{2}$ .

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Step 2.1

Factor $m^{2}$ out of $m^{4} n^{3}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $m^{2}$ out of $m^{2} n^{5}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $n^{3}$ and $n^{5}$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $n^{3}$ out of $n^{5}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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