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.

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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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.