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

Verified step by step guidance

1. Identify the base and the exponent in the expression. Here, the base is \((-2)\) and the exponent is \$6$.
2. 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 \((-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2)\).
3. 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.
4. 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.
5. Write the final product after completing all multiplications to find the value of \((-2)^6\).

Key Concepts

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.