Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Radical Expressions
2:55 minutes
Problem 8c
Textbook Question
Textbook QuestionDetermine whether each statement is true or false. If false, correct the right side of the equation. (m^2/3)(m^1/3) = m^2/9
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents and Their Properties
Understanding exponents is crucial in algebra, particularly the rules governing their manipulation. The product of powers rule states that when multiplying two expressions with the same base, you add their exponents. For example, m^a * m^b = m^(a+b). This principle is essential for simplifying expressions involving exponents.
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Simplifying Expressions
Simplifying expressions involves reducing them to their most basic form, which often requires applying algebraic rules. In the context of exponents, this means combining like terms and using exponent rules to rewrite expressions. For instance, (m^2/3)(m^1/3) can be simplified by adding the exponents, leading to m^(2/3 + 1/3).
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True or False Statements in Algebra
Determining the truth value of algebraic statements requires a solid understanding of the underlying mathematical principles. A statement is true if both sides of the equation are equal after simplification. If they are not, the statement is false, and one must find the correct expression that makes the equation valid.
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