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

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Identify the order of operations to evaluate the expression correctly. Remember the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Evaluate the exponent first: calculate \((-2)^3\). This means raising -2 to the power of 3.

Next, perform the multiplication: calculate \(7 \times 3\).

Now substitute the results back into the expression and simplify the expression from left to right, handling addition and subtraction accordingly.

Combine all the terms step-by-step to get the simplified expression, ensuring you carefully handle the signs (positive and negative) during addition and subtraction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Order of Operations (PEMDAS/BODMAS)

The order of operations dictates the sequence in which mathematical operations are performed: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). This ensures consistent and correct evaluation of expressions.

Exponents

Exponents represent repeated multiplication of a base number. For example, (-2)³ means multiplying -2 by itself three times: (-2) × (-2) × (-2). Understanding how to evaluate exponents, especially with negative bases, is crucial.

Multiplication and Subtraction

After handling parentheses and exponents, multiplication and subtraction are performed from left to right. Recognizing how to correctly multiply and subtract signed numbers is essential to accurately simplify the expression.

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