Evaluate each expression. See Example 4. -2⁴

검증된 단계별 안내

Identify the expression to evaluate: $-2^4$.

Recall the order of operations (PEMDAS/BODMAS): exponents are evaluated before multiplication or negation.

Evaluate the exponent first: calculate \$2^4$, which means $2 \times 2 \times 2 \times 2$.

After finding \$2^4$, apply the negative sign in front of the result, since the negative sign is not inside the exponentiation.

Write the final expression as $- (2^4)$ and simplify accordingly.

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주요 개념

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

Order of Operations (PEMDAS)

The order of operations dictates the sequence in which mathematical operations are performed: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). This ensures consistent and correct evaluation of expressions.

Exponents and Powers

An exponent indicates how many times a base number is multiplied by itself. For example, 4⁴ means 4 × 4 × 4 × 4. Understanding how to compute powers is essential for evaluating expressions involving exponents.

Negative Signs and Exponents

A negative sign before a base with an exponent can change the result depending on parentheses. For example, -2⁴ means the negative of 2⁴, which is -16, while (-2)⁴ means (-2) multiplied four times, resulting in 16. Recognizing this distinction is crucial.