Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

0. Review of College Algebra

Solving Linear Equations

Trigonometry

0. Review of College Algebra

Solving Linear Equations

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1:13 minutes

Problem 69

Textbook Question

Concept Check Evaluate each exponential expression.a. 8²b. -8²c. (-8)²d. -(-8)²

Verified step by step guidance

Step 1: Understand the concept of exponents. An exponent indicates how many times a number, known as the base, is multiplied by itself.

Step 2: For part (a), 8², calculate 8 multiplied by itself.

Step 3: For part (b), -8², recognize that the negative sign is not included in the base, so calculate 8² first and then apply the negative sign.

Step 4: For part (c), (-8)², note that the negative sign is included in the base, so multiply -8 by itself.

Step 5: For part (d), -(-8)², first calculate (-8)² as in part (c), then apply the negative sign to the result.

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Key Concepts

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

Exponential Notation

Exponential notation is a mathematical shorthand that represents repeated multiplication of a number by itself. For example, in the expression 8², the base 8 is multiplied by itself, resulting in 64. Understanding how to interpret and calculate exponential expressions is crucial for evaluating them correctly.

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 acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. This concept is essential for evaluating expressions with multiple operations, such as those involving exponents and negative signs.

Negative Numbers and Squaring

When squaring a negative number, the result is always positive because multiplying two negative numbers yields a positive product. For instance, (-8)² equals 64, while -8² is interpreted as -(8²), resulting in -64. Understanding how to handle negative signs in conjunction with exponents is vital for accurately evaluating expressions.