Basic Math Examples

$\frac{{(m^{5} n^{- 2})}^{6}}{m^{4} n^{- 3}}$

Step 1

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

$\frac{{(m^{5} n^{- 2})}^{6} n^{3}}{m^{4}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $m^{5} n^{- 2}$ .

$\frac{{(m^{5})}^{6} {(n^{- 2})}^{6} n^{3}}{m^{4}}$

Step 2.2

Multiply the exponents in ${(m^{5})}^{6}$ .

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Step 2.2.1

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

$\frac{m^{5 \cdot 6} {(n^{- 2})}^{6} n^{3}}{m^{4}}$

Step 2.2.2

Multiply $5$ by $6$ .

$\frac{m^{30} {(n^{- 2})}^{6} n^{3}}{m^{4}}$

Step 2.3

Multiply the exponents in ${(n^{- 2})}^{6}$ .

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Step 2.3.1

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

$\frac{m^{30} n^{- 2 \cdot 6} n^{3}}{m^{4}}$

Step 2.3.2

Multiply $- 2$ by $6$ .

$\frac{m^{30} n^{- 12} n^{3}}{m^{4}}$

Step 2.4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{m^{30} \frac{1}{n^{12}} n^{3}}{m^{4}}$

Step 2.5

Combine exponents.

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Step 2.5.1

Combine $m^{30}$ and $\frac{1}{n^{12}}$ .

$\frac{\frac{m^{30}}{n^{12}} n^{3}}{m^{4}}$

Step 2.5.2

Combine $\frac{m^{30}}{n^{12}}$ and $n^{3}$ .

$\frac{\frac{m^{30} n^{3}}{n^{12}}}{m^{4}}$

Step 2.6

Reduce the expression $\frac{m^{30} n^{3}}{n^{12}}$ by cancelling the common factors.

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Step 2.6.1

Factor $n^{3}$ out of $m^{30} n^{3}$ .

$\frac{\frac{n^{3} m^{30}}{n^{12}}}{m^{4}}$

Step 2.6.2

Factor $n^{3}$ out of $n^{12}$ .

$\frac{\frac{n^{3} m^{30}}{n^{3} n^{9}}}{m^{4}}$

Step 2.6.3

Cancel the common factor.

$\frac{\frac{n^{3} m^{30}}{n^{3} n^{9}}}{m^{4}}$

Step 2.6.4

Rewrite the expression.

$\frac{\frac{m^{30}}{n^{9}}}{m^{4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{m^{30}}{n^{9}} \cdot \frac{1}{m^{4}}$

Step 4

Combine.

$\frac{m^{30} \cdot 1}{n^{9} m^{4}}$

Step 5

Cancel the common factor of $m^{30}$ and $m^{4}$ .

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Step 5.1

Factor $m^{4}$ out of $m^{30} \cdot 1$ .

$\frac{m^{4} (m^{26} \cdot 1)}{n^{9} m^{4}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $m^{4}$ out of $n^{9} m^{4}$ .

$\frac{m^{4} (m^{26} \cdot 1)}{m^{4} n^{9}}$

Step 5.2.2

Cancel the common factor.

$\frac{m^{4} (m^{26} \cdot 1)}{m^{4} n^{9}}$

Step 5.2.3

Rewrite the expression.

$\frac{m^{26} \cdot 1}{n^{9}}$

Step 6

Multiply $m^{26}$ by $1$ .

$\frac{m^{26}}{n^{9}}$