Evaluate each expression. (-2)6

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 84

1장, 문제 84

Evaluate each expression. (-2)⁶

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Identify the base and the exponent in the expression $(-2)^6$. Here, the base is $-2$ and the exponent is $6$.

Recall that an exponent indicates how many times the base is multiplied by itself. So, $(-2)^6$ means $(-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2)$.

Since the exponent is even, multiplying a negative number an even number of times results in a positive number. This is because each pair of negative factors multiplies to a positive.

Calculate the value of \$2^6$ by multiplying $2$ by itself six times: $2 \times 2 \times 2 \times 2 \times 2 \times 2$.

Combine the sign consideration from step 3 with the magnitude from step 4 to determine the final value of $(-2)^6$.

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주요 개념

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

Exponents and Powers

An exponent indicates how many times a base number is multiplied by itself. For example, in (-2)^6, the base is -2 and the exponent 6 means multiplying -2 by itself six times.

Negative Base with Even Exponent

When a negative number is raised to an even exponent, the result is positive because multiplying an even number of negative factors results in a positive product.

Order of Operations and Parentheses

Parentheses indicate that the negative sign is part of the base. Thus, (-2)^6 means the entire -2 is raised to the 6th power, unlike -2^6, which would mean the negative of 2 raised to the 6th power.