Evaluate each exponential expression in Exercises 1–22. (−3)⁰

Verified step by step guidance

1. Recall the zero exponent rule, which states that for any nonzero base \(a\), \(a^0 = 1\).
2. Identify the base in the expression \((\-3)^0\). Here, the base is \(-3\).
3. Since \(-3\) is a nonzero number, apply the zero exponent rule: \((\-3)^0 = 1\).
4. Understand that the parentheses indicate the entire number \(-3\) is raised to the zero power, not just the 3.
5. Conclude that the value of \((\-3)^0\) is 1, based on the zero exponent rule.

Key Concepts

Exponents and Powers

Exponents indicate how many times a base number is multiplied by itself. For example, in a^n, 'a' is the base and 'n' is the exponent, meaning multiply 'a' by itself 'n' times. Understanding this helps evaluate expressions like (−3)^0.

Zero Exponent Rule

Any nonzero base raised to the zero power equals 1. This means that for any number 'a' ≠ 0, a^0 = 1. This rule applies regardless of whether the base is positive or negative, so (−3)^0 = 1.

Order of Operations with Exponents

When evaluating expressions with exponents, apply the exponent before other operations like multiplication or addition. Parentheses indicate that the exponent applies to the entire base, so (−3)^0 means the whole number −3 is raised to the zero power.