Basic Math Examples

$\frac{{(m^{7} n^{3})}^{3}}{m^{14} n^{21}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $m^{7} n^{3}$ .

$\frac{{(m^{7})}^{3} {(n^{3})}^{3}}{m^{14} n^{21}}$

Step 1.2

Multiply the exponents in ${(m^{7})}^{3}$ .

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Step 1.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{m^{7 \cdot 3} {(n^{3})}^{3}}{m^{14} n^{21}}$

Step 1.2.2

Multiply $7$ by $3$ .

$\frac{m^{21} {(n^{3})}^{3}}{m^{14} n^{21}}$

Step 1.3

Multiply the exponents in ${(n^{3})}^{3}$ .

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Step 1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{m^{21} n^{3 \cdot 3}}{m^{14} n^{21}}$

Step 1.3.2

Multiply $3$ by $3$ .

$\frac{m^{21} n^{9}}{m^{14} n^{21}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $m^{21}$ and $m^{14}$ .

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Step 2.1.1

Factor $m^{14}$ out of $m^{21} n^{9}$ .

$\frac{m^{14} (m^{7} n^{9})}{m^{14} n^{21}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $m^{14}$ out of $m^{14} n^{21}$ .

$\frac{m^{14} (m^{7} n^{9})}{m^{14} (n^{21})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{m^{14} (m^{7} n^{9})}{m^{14} n^{21}}$

Step 2.1.2.3

Rewrite the expression.

$\frac{m^{7} n^{9}}{n^{21}}$

Step 2.2

Cancel the common factor of $n^{9}$ and $n^{21}$ .

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Step 2.2.1

Factor $n^{9}$ out of $m^{7} n^{9}$ .

$\frac{n^{9} m^{7}}{n^{21}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $n^{9}$ out of $n^{21}$ .

$\frac{n^{9} m^{7}}{n^{9} n^{12}}$

Step 2.2.2.2

Cancel the common factor.

$\frac{n^{9} m^{7}}{n^{9} n^{12}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{m^{7}}{n^{12}}$