Evaluate each expression. See Example 4.(-3)⁵

Verified step by step guidance

1. Identify the base and the exponent in the expression \((-3)^5\).
2. Understand that the base is \(-3\) and the exponent is \(5\), which means you need to multiply \(-3\) by itself 5 times.
3. Write the expression as \((-3) \times (-3) \times (-3) \times (-3) \times (-3)\).
4. Recall that multiplying two negative numbers results in a positive number, and multiplying a positive number by a negative number results in a negative number.
5. Calculate the product step by step, keeping track of the sign changes with each multiplication.

Key Concepts

Exponents

Exponents represent repeated multiplication of a number by itself. For example, in the expression a^n, 'a' is the base and 'n' is the exponent, indicating how many times 'a' is multiplied by itself. Understanding how to manipulate exponents, including negative bases and odd/even powers, is crucial for evaluating expressions like (-3)⁵.

Negative Numbers

Negative numbers are values less than zero, and they can affect the outcome of mathematical operations, especially when raised to a power. When a negative number is raised to an odd exponent, the result remains negative, while raising it to an even exponent results in a positive value. This concept is essential for correctly evaluating expressions involving 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. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating expressions like (-3)⁵, recognizing that exponents are calculated before multiplication or addition is vital.