Textbook Question
Evaluate each expression. See Example 4. (-2)⁴
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem R.2.87
Evaluate each expression. See Example 5. 5 - 7 • 3 - (-2)³
Verified step by step guidance1
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.
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04:12
Algebraic Operations on Vectors
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.
Recommended video:
4:28Introduction to Inverse Trig Functions
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.
Recommended video:
3:18Adding and Subtracting Complex Numbers
Related Practice
Textbook Question
Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 5k + 3k
Textbook Question
Evaluate each expression. See Example 5. 6 • 3 - 12 ÷ 4
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Textbook Question
Simplify each expression. See Example 8. -6p + 5 - 4p + 6 + 11p
Textbook Question
Evaluate each expression. See Example 4. -2⁴
Textbook Question
Evaluate each expression. See Example 5. -8 + (-4) (-6) ÷ 12 4 - (-3)