In Exercises 59–70, evaluate each exponential expression. (-2)^3

Verified step by step guidance

1. Identify the base and the exponent in the expression \((-2)^3\). Here, the base is \(-2\) and the exponent is \(3\).
2. Understand that the exponent \(3\) indicates that the base \(-2\) should be multiplied by itself a total of three times.
3. Write the expression as a multiplication of the base: \((-2) \times (-2) \times (-2)\).
4. Calculate the product of the first two factors: \((-2) \times (-2)\). Remember that multiplying two negative numbers results in a positive number.
5. Multiply the result from the previous step by the remaining factor \(-2\) to complete the evaluation of the expression.

Key Concepts

Exponential Expressions

Exponential expressions involve a base raised to a power, indicating how many times the base is multiplied by itself. For example, in the expression a^n, 'a' is the base and 'n' is the exponent. Understanding how to evaluate these expressions is crucial, as it involves both multiplication and the properties of exponents.

Negative Bases

When dealing with negative bases, such as (-2), the evaluation of the expression depends on whether the exponent is even or odd. An odd exponent will yield a negative result, while an even exponent will yield a positive result. This distinction is important for accurately calculating the value of expressions with negative bases.

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 expressions, one must follow the order: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). This principle is essential for correctly solving exponential expressions.