The word product means to multiply. The product rule of exponents helps us remember what we do when two numbers with exponents are multiplied together. Here are some math vocabulary words that will help you to understand this lesson better:

- Base = the number or variable that is being multiplied to itself.
- Power = the number of the exponent, how many times the base is multiplied to itself.

The following video will explain, with some examples, what the product rule is; the word product in math means what you get when you multiply things together.

\(\text{x}^3\,\text{x}^4 = \text{x}^7 \)

Video Source (07:19 mins) | Transcript

Qualification for the product rule: bases must be the same. If the bases are the same, then the product rule says that you add the exponents. Also remember that you can multiply in any order, so \( (a)(b) = (b)(a) \). This means that if there are multiple bases, you can rearrange the order and add the exponents of any of the bases that are the same.

## Additional Resources

- Khan Academy: Exponent Rules Introduction (09:42 mins, Transcript)
- Khan Academy: Exponent Properties 1 (02:35 mins, Transcript)
- Khan Academy: Exponent Properties with Products (13:59 mins, Transcript)

### Practice Problems

**Simplify the following Expressions:**

- \(\text{x}\,{\text{x}}^{3}\) (Solution
- \({\text{m}}^{2}\,{\text{m}}^{5}\) (Solution
- \({\text{m}}^{3}\,{\text{x}}^{6}\,{\text{m}}\) (Video Solution
- \({\text{x}}^{2}\,{\text{y}}^{3}\,{\text{x}}^{4}\) (Solution
- \({\text{mx}}^{2}\,{\text{m}}^{3}\,{\text{x}}^{7}\) (Solution
- \({\text{x}}^{5}\,{\text{y}}^{4}\,{\text{x}}^{2}\,{\text{y}}\,{\text{z}}^{2}\) (Video Solution

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