Algebra Examples

$m^{19} n^{19} {(\frac{1}{m})}^{30} {(\frac{1}{n})}^{30}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{1}{m}$ .

$m^{19} n^{19} \frac{1^{30}}{m^{30}} {(\frac{1}{n})}^{30}$

Step 1.2

One to any power is one.

$m^{19} n^{19} \frac{1}{m^{30}} {(\frac{1}{n})}^{30}$

Step 2

Cancel the common factor of $m^{19}$ .

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Step 2.1

Factor $m^{19}$ out of $m^{19} n^{19}$ .

$m^{19} (n^{19}) \frac{1}{m^{30}} {(\frac{1}{n})}^{30}$

Step 2.2

Factor $m^{19}$ out of $m^{30}$ .

$m^{19} (n^{19}) \frac{1}{m^{19} m^{11}} {(\frac{1}{n})}^{30}$

Step 2.3

Cancel the common factor.

$m^{19} n^{19} \frac{1}{m^{19} m^{11}} {(\frac{1}{n})}^{30}$

Step 2.4

Rewrite the expression.

$n^{19} \frac{1}{m^{11}} {(\frac{1}{n})}^{30}$

Step 3

Combine $n^{19}$ and $\frac{1}{m^{11}}$ .

$\frac{n^{19}}{m^{11}} {(\frac{1}{n})}^{30}$

Step 4

Apply the product rule to $\frac{1}{n}$ .

$\frac{n^{19}}{m^{11}} \cdot \frac{1^{30}}{n^{30}}$

Step 5

Combine.

$\frac{n^{19} \cdot 1^{30}}{m^{11} n^{30}}$

Step 6

Cancel the common factor of $n^{19}$ and $n^{30}$ .

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Step 6.1

Factor $n^{19}$ out of $n^{19} \cdot 1^{30}$ .

$\frac{n^{19} (1^{30})}{m^{11} n^{30}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $n^{19}$ out of $m^{11} n^{30}$ .

$\frac{n^{19} (1^{30})}{n^{19} (m^{11} n^{11})}$

Step 6.2.2

Cancel the common factor.

$\frac{n^{19} \cdot 1^{30}}{n^{19} (m^{11} n^{11})}$

Step 6.2.3

Rewrite the expression.

$\frac{1^{30}}{m^{11} n^{11}}$

Step 7

One to any power is one.

$\frac{1}{m^{11} n^{11}}$