Evaluate each expression. -35

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 82

1장, 문제 82

Evaluate each expression. -3⁵

검증된 단계별 안내

Recognize that the expression is \(-3^5\), which means the exponent applies only to the 3, not the negative sign, because there are no parentheses around \(-3\).

Rewrite the expression as \(-(3^5)\) to clarify the order of operations: the exponent is evaluated first, then the negative sign is applied.

Calculate \(3^5\), which means multiplying 3 by itself 5 times: \(3 \times 3 \times 3 \times 3 \times 3\).

After finding the value of \(3^5\), apply the negative sign to that result to get the final value of the expression.

Write the final expression as \(- (3^5)\) and substitute the calculated value of \(3^5\) to complete the evaluation.

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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 parts of a mathematical expression are evaluated. Exponents are calculated before multiplication or negation unless parentheses indicate otherwise. 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, 3^5 means 3 × 3 × 3 × 3 × 3. Understanding how to compute powers is essential for evaluating expressions involving exponents.

Negative Signs and Exponents

A negative sign in front of a base without parentheses is treated as multiplication by -1 after exponentiation. For example, -3^5 means -(3^5), not (-3)^5. Parentheses change this order, affecting the final result.