Evaluate each expression. -24

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 81

1장, 문제 81

Evaluate each expression. -2⁴

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Recognize the order of operations: exponents are evaluated before multiplication or negation.

Rewrite the expression to clarify the operation: the expression -2^4 means the negative of 2 raised to the 4th power, which can be written as $- (2^4)$.

Calculate the exponent part first: compute \$2^4$, which means multiplying 2 by itself 4 times.

After finding \$2^4$, apply the negative sign in front of the result.

Write the final expression as $- (2^4)$ and simplify to get the evaluated value.

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주요 개념

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

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed. Exponents are evaluated before multiplication or negation, so in the expression -2^4, the exponent applies to 2 first, then the negative sign is applied.

Exponents

An exponent indicates how many times a base number is multiplied by itself. For example, 2^4 means 2 × 2 × 2 × 2, which equals 16. Understanding exponents is essential to correctly evaluate expressions involving powers.

Negative Sign and Exponents

A negative sign in front of a base with an exponent can change the result depending on parentheses. Without parentheses, -2^4 means the negative of 2^4, which is -16. With parentheses, (-2)^4 means (-2) multiplied four times, resulting in a positive 16.