Precalculus Examples

$\frac{s^{12} n^{- 10}}{s^{8} n^{- 7}}$

Step 1

Move $n^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{s^{12}}{s^{8} n^{- 7} n^{10}}$

Step 2

Multiply $n^{- 7}$ by $n^{10}$ by adding the exponents.

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Step 2.1

Move $n^{10}$ .

$\frac{s^{12}}{s^{8} (n^{10} n^{- 7})}$

Step 2.2

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

$\frac{s^{12}}{s^{8} n^{10 - 7}}$

Step 2.3

Subtract $7$ from $10$ .

$\frac{s^{12}}{s^{8} n^{3}}$

Step 3

Cancel the common factor of $s^{12}$ and $s^{8}$ .

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Step 3.1

Factor $s^{8}$ out of $s^{12}$ .

$\frac{s^{8} s^{4}}{s^{8} n^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $s^{8}$ out of $s^{8} n^{3}$ .

$\frac{s^{8} s^{4}}{s^{8} (n^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{s^{8} s^{4}}{s^{8} n^{3}}$

Step 3.2.3

Rewrite the expression.

$\frac{s^{4}}{n^{3}}$