Evaluate each expression. See Example 5. 5 - 7 • 3 - (-2)³

Verified step by step guidance

1. Identify the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
2. Evaluate the exponent: Calculate $(-2{)}^3$.
3. Perform the multiplication: Calculate $7\cdot 3$.
4. Perform the subtraction and addition in order from left to right: Start with $5-\text{(result from multiplication)}$.
5. Add the result of the exponentiation to the previous result.

Key Concepts

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. Following these rules is crucial when evaluating expressions to avoid errors.

Exponents

Exponents represent repeated multiplication of a number by itself. For example, (-2)³ means -2 multiplied by itself three times, resulting in -8. Understanding how to calculate exponents is essential for simplifying expressions that include powers, as they can significantly affect the outcome of the evaluation.

Negative Numbers

Negative numbers are values less than zero and can affect calculations in various ways, especially when involved in operations like addition, subtraction, and exponentiation. For instance, subtracting a negative number is equivalent to adding its positive counterpart. Recognizing how to handle negative numbers is vital for accurately evaluating expressions that include them.