Basic Math Examples

$\frac{4 m^{- 5} n^{11}}{10 m^{- 3} n^{- 4}}$

Step 1

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

$\frac{4 n^{11}}{10 m^{- 3} n^{- 4} m^{5}}$

Step 2

Multiply $m^{- 3}$ by $m^{5}$ by adding the exponents.

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Step 2.1

Move $m^{5}$ .

$\frac{4 n^{11}}{10 (m^{5} m^{- 3}) n^{- 4}}$

Step 2.2

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

$\frac{4 n^{11}}{10 m^{5 - 3} n^{- 4}}$

Step 2.3

Subtract $3$ from $5$ .

$\frac{4 n^{11}}{10 m^{2} n^{- 4}}$

Step 3

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

$\frac{4 n^{11} n^{4}}{10 m^{2}}$

Step 4

Multiply $n^{11}$ by $n^{4}$ by adding the exponents.

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Step 4.1

Move $n^{4}$ .

$\frac{4 (n^{4} n^{11})}{10 m^{2}}$

Step 4.2

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

$\frac{4 n^{4 + 11}}{10 m^{2}}$

Step 4.3

Add $4$ and $11$ .

$\frac{4 n^{15}}{10 m^{2}}$

Step 5

Cancel the common factor of $4$ and $10$ .

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Step 5.1

Factor $2$ out of $4 n^{15}$ .

$\frac{2 (2 n^{15})}{10 m^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $10 m^{2}$ .

$\frac{2 (2 n^{15})}{2 (5 m^{2})}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (2 n^{15})}{2 (5 m^{2})}$

Step 5.2.3

Rewrite the expression.

$\frac{2 n^{15}}{5 m^{2}}$