Division is the opposite of multiplication because when \(5 \times 3 = 15 \), then \(15 \div 5 = 3 \). Similarly, the exponent rule of division (quotient rule) is the opposite of the product rule. Here is one math vocabulary word that will help you to understand this lesson video better:

- Quotient = what you get when you divide a number by another number

The following video will explain with some examples of how to divide with exponents:

Video Source (05:37 mins) | Transcript

Just like with the product rule, in order to use the quotient rule, our bases must be the same. Then, if the bases are the same, the division rule says we subtract the power of the denominator from the power of the numerator.

Examples:

\(\displaystyle \frac{{\text{m}}^6}{{\text{m}}^2}={\text{m}}^{6-2}={\text{m}}^4\)

\(\displaystyle \frac{{\text{x}}^2{\text{m}}^3{\text{x}}^3}{{\text{m}}^2{\text{x}}}=\frac{{\text{x}}^{2+3}{\text{m}}^3}{{\text{m}}^2{\text{x}}}={\text{x}}^{5-1}{\text{m}}^{3-2}={\text{x}}^4{\text{m}}\)

## Additional Resources

- Khan Academy: Exponent Properties 2 (05:11 mins, Transcript)
- Khan Academy: Exponent Properties with Quotients (09:22 mins, Transcript)

### Practice Problems

**Simplify the following expressions:**

- \(\dfrac{{\text{m}}^{5}}{{\text{m}}^{2}}\) (Solution
- \(\dfrac{{\text{x}}^{7}}{{\text{x}}^{5}}\) (Solution
- \(\dfrac{{\text{m}}^{2}{\text{x}}^{2}}{\text{xm}}\) (Solution
- \(\dfrac{{\text{x}}^{2}{\text{y}}^{4}{\text{x}}^{7}}{{\text{xy}}^{3}}\) (Solution
- \(\dfrac{{\text{x}}^{2}{\text{m}}^{3}{\text{x}}^{4}}{{\text{m}}^{2}{\text{x}}^{3}}\) (Video Solution
- \(\dfrac{{\text{x}}^{5}{\text{y}}^{2}{\text{x}}}{{\text{x}}^{2}{\text{yz}}}\) (Video Solution

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