Evaluate each expression. See Example 4.-2⁴

Verified step by step guidance

1. Identify the base and the exponent in the expression: The base is -2 and the exponent is 4.
2. Understand that the expression -2^4 means (-2) multiplied by itself 4 times.
3. Write the expression as a multiplication: (-2) * (-2) * (-2) * (-2).
4. Recall that multiplying two negative numbers results in a positive number.
5. Multiply the numbers step by step: First, (-2) * (-2) = 4, then 4 * (-2) = -8, and finally, -8 * (-2) = 16.

Key Concepts

Exponents

Exponents represent the number of times a base is multiplied by itself. For example, in the expression -2⁴, the base is -2 and the exponent is 4, indicating that -2 is multiplied by itself four times: -2 × -2 × -2 × -2. Understanding how to evaluate exponents is crucial for simplifying expressions and performing calculations accurately.

Negative Bases

When dealing with negative bases, the sign of the result depends on whether the exponent is even or odd. An even exponent, like in -2⁴, results in a positive value because the negative signs cancel each other out. Conversely, an odd exponent would yield a negative result. This concept is essential for correctly interpreting and calculating expressions involving negative numbers.

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. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating -2⁴, recognizing that exponents are calculated before multiplication or addition is vital for arriving at the correct answer.