Evaluate each exponential expression in Exercises 1–22. (−2)⁶

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

Recall that raising a number to an exponent means multiplying the base by itself as many times as the exponent indicates. 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 step-by-step by pairing the factors: for example, \((-2) \times (-2) = 4\), then multiply the result by the next \((-2)\), and so on until all six factors are multiplied.

Write the final product after completing all multiplications to find the value of \((-2)^6\).

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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51s

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주요 개념

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

Exponents and Powers

Exponents indicate 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 entire base, including the negative sign, is raised to the exponent. Without parentheses, only the number is raised to the power, and the negative sign is applied afterward.

Evaluate each exponential expression in Exercises 1–22. (−2)6