Match each expression in Column I with its equivalent expression in Column II. Choices may be used once, more than once, or not at all.

Verified step by step guidance

1. Recall the zero exponent rule: For any nonzero number \(a\), \(a^0 = 1\). This will help evaluate expressions like \$6^0\(, \)(-6)^0$, etc.
2. Evaluate each expression in Column I using the zero exponent rule and paying attention to the placement of the negative sign:
3. a. \$6^0\(: Since 6 is nonzero, \)6^0 = 1$.
4. b. \(-6^0\): Here, the exponent applies only to 6, so \$6^0 = 1\(, then apply the negative sign outside, so \)-6^0 = -1$.
5. c. \((-6)^0\): The entire quantity \(-6\) is raised to the zero power, so \((-6)^0 = 1\).
6. d. \(-(-6)^0\): First evaluate \((-6)^0 = 1\), then apply the negative sign outside, so \(-(-6)^0 = -1\).
7. Match each evaluated result with the options in Column II: 0, 1, -1, 6, -6.

Key Concepts

Zero Exponent Rule

Any nonzero base raised to the zero power equals 1. For example, 6^0 = 1 and (-6)^0 = 1. This rule is fundamental for simplifying expressions involving exponents.

Order of Operations with Exponents and Negatives

When evaluating expressions like -6^0, the exponent applies before the negative sign. So, 6^0 is evaluated first (which is 1), then the negative sign is applied, resulting in -1.

Parentheses Affecting Exponentiation

Parentheses change the base of the exponent. For example, (-6)^0 means the entire -6 is raised to zero, giving 1, while -6^0 means the negative of 6^0, which is -1. Understanding this distinction is key.