The power rule is about a base raised to a power, all raised to another power. What does this mean? This means everything raised to the interior exponent is then multiplied together the number of times of the exterior exponent.

Example:

\(\left (2^{3} \right )^{4} = 2^{(3\cdot4)} = 2^{12}\)

Rules of Exponents - Power Rule

Video Source (08:23 mins) | Transcript

Things to remember: with the power rule, the powers multiply. Everything within the parentheses is affected by the power.

## Additional Resources

- Khan Academy: Exponent Properties 3 (02:34 mins, Transcript)
- Khan Academy: Exponent Properties with parentheses (05:57 mins, Transcript)

### Practice Problems

**Simplify the following expressions:**

- \(({\text{x}}^{\text{m}})^{\text{n}}\) (Solution
- \((3^{2})^{3}\) (Solution
- \(({\text{m}}^{2})^{4}({\text{y}}^{5})^{2}\) (Solution
- \(({\text{x}}^{3})^{2}({\text{y}}^{4})^{2}(x^{2})^{1}\) (Video Solution
- \((4^{2})^{3}(2^{5})^{1}\) (Video Solution
- \(({\text{a}}^{\text{x}})^{2}({\text{b}}^{3})^{2}\) (Solution

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