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

Recall the zero exponent rule: For any nonzero number $a$, $a^0 = 1$. This will help evaluate expressions like \$6^0$, $(-6)^0$, etc.

Evaluate each expression in Column I using the zero exponent rule and paying attention to the placement of the negative sign:

a. \$6^0$: Since 6 is nonzero, $6^0 = 1$.

b. $-6^0$: Here, the exponent applies only to 6, so $6^0 = 1$, then apply the negative sign outside, so $-6^0 = -1$.

c. $(-6)^0$: The entire quantity $-6$ is raised to the zero power, so $(-6)^0 = 1$.

d. $-(-6)^0$: First evaluate $(-6)^0 = 1$, then apply the negative sign outside, so $-(-6)^0 = -1$.

Match each evaluated result with the options in Column II: 0, 1, -1, 6, -6.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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