What happens when we multiply (−1) to itself multiple times? There is a pattern to find that makes simplifying exponent problems with a negative base much more simple.

Rules of Exponents--(-1) Raised to an Exponent

Video Source (07:57 mins) | Transcript

Negative next to a number vs negative in parentheses

Video Source (08:22 mins) | Transcript

The basic rule when a negative number is raised to an exponent \( (−b)^x \):

- If the power is even → the answer is positive.
- If the power is odd → the answer is negative.

It is important to know that \( −b^x \) is different than \( (−b)^x \). When you have \( −b^x \) , where the negative is not inside the parentheses, the exponent does not apply to it. This is because of the order of operations.

## Additional Resources

- Khan Academy: Exponents with Negative Bases (04:29 mins, Transcript)

### Practice Problems

**Evaluate the following expressions:**

- \(({-}1)^{5}=?\) (Solution
- \(({-}1)^{4}=?\) (Solution
- \(({-}1)^{105}=?\) (Solution
- \(({-}1)^{236}=?\) (Solution
- \(({-}5)^{3}=?\) (Video Solution
- \(({-}7)^{4}=?\) (Solution
- \((-{\text{a}})^{6}=?\) (Video Solution
- \(-1^{2}=?\) (Solution
- \(-2^{4}=?\) (Solution

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