Evaluate each expression. (-2)^6

Verified step by step guidance

1. Identify the base and the exponent in the expression \((-2)^6\). The base is \(-2\) and the exponent is 6.
2. Understand that the exponent indicates how many times the base is multiplied by itself. So, \((-2)^6\) means \((-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2)\).
3. Calculate the product step by step: First, multiply the first two terms: \((-2) \times (-2) = 4\).
4. Continue multiplying the result by the next \(-2\): \(4 \times (-2) = -8\).
5. Repeat this process until all terms are multiplied: \(-8 \times (-2) = 16\), \(16 \times (-2) = -32\), \(-32 \times (-2) = 64\).

Key Concepts

Exponents

Exponents represent the number of times a base is multiplied by itself. In the expression (-2)^6, the base is -2, and the exponent is 6, indicating that -2 should be multiplied by itself six times. Understanding how to apply exponents is crucial for evaluating expressions involving powers.

Negative Base

When dealing with a negative base raised to an even exponent, the result is positive. In this case, (-2)^6 results in a positive value because multiplying an even number of negative factors yields a positive product. Recognizing the behavior of negative bases in exponentiation is essential for accurate calculations.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. In evaluating (-2)^6, it is important to follow these rules, which prioritize exponentiation before multiplication or addition, ensuring the expression is simplified correctly.