Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 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
1:55 minutes
Problem 23a
Textbook Question
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (2²)⁵
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents and Powers
Exponents represent repeated multiplication of a base number. The expression a^n means 'a multiplied by itself n times.' Understanding the laws of exponents, such as the power of a power rule (a^(m*n) = (a^m)^n), is crucial for simplifying expressions involving exponents.
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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, emphasizing that exponents should be calculated before multiplication or addition.
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Simplification of Expressions
Simplification involves reducing an expression to its simplest form while maintaining its value. This often includes combining like terms, applying exponent rules, and eliminating unnecessary parentheses. In the case of (2²)⁵, applying the power of a power rule simplifies the expression effectively.
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