What does it mean if our exponent is negative? Can you multiply a number to itself a negative amount of times? Instead of trying to wrap our brains around what that would mean, we use the exponent rule of division (quotient rule) to learn what a negative exponent means.

Video Source (07:39 mins) | Transcript

As explained in the video, when we have a negative exponent we can simply move it to the other part of the fraction (from top to bottom or bottom to top) and then it will be a positive exponent. When doing your practice problems, remember you can use these rules in any order (product, quotient, and negative exponents) to simplify your expression. Many people like to use the negative exponent rule first because it’s less confusing to do the product and division rules once you don’t have any negative exponents.

## Additional Resources

- Khan Academy: Negative Exponents (07:13 mins, Transcript)
- Khan Academy: Negative Exponent Intuition (04:37 mins, Transcript)

### Practice Problems

- Which expression is equivalent to \({\text{x}}^{-2}\) ? (Solution
- \(\dfrac{1}{{\text{x}}^{2}}\)
- \(\dfrac{1}{{\text{x}}^{-2}}\)
- \(\dfrac{1^{2}}{\text{x}}\)
- \(\dfrac{2}{\text{x}}\)

- Which expression is equivalent to \({\text{b}}^{-9}\) ? (Solution
- \(\dfrac{1}{{\text{b}}^{-9}}\)
- \(\dfrac{1^{9}}{\text{b}}\)
- \(\dfrac{1}{{\text{b}}^{9}}\)
- \(\dfrac{9}{\text{b}}\)

- Write the expression \(\dfrac{{\text{y}}^{-7}}{{\text{y}}^{-13}}\) using only positive exponents and simplify. (Solution
- Write the expression \(\dfrac{{\text{m}}^{-5}{\text{x}}^{3}}{{\text{x}}^{-2}{\text{m}}^{-2}}\) using only positive exponents and simplify. (Solution
- Simplify the expression \(\dfrac{{\text{a}}^{7}{\text{b}}^{2}{\text{a}}^{-2}}{{\text{a}}^{-3}{\text{b}}^{7}}\). (Video Solution
- Simplify the expression \(\dfrac{{\text{x}}^{-5}{\text{y}}^{-3}{\text{z}}^{-2}}{{\text{x}}^{3}{\text{y}}^{-4}}\). (Video Solution

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