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
3:42 minutes
Problem 57d
Textbook Question
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 16^¾ 16^¼
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Exponents
Rational exponents are a way to express roots using fractional powers. For example, an exponent of 1/n indicates the n-th root of a number. Thus, a rational exponent like ¾ can be interpreted as taking the cube root of a number and then squaring the result. Understanding this concept is essential for simplifying expressions involving rational exponents.
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Properties of Exponents
The properties of exponents include rules that govern how to manipulate expressions with exponents. Key properties include the product of powers (a^m * a^n = a^(m+n)), the power of a power ( (a^m)^n = a^(m*n)), and the power of a product ( (ab)^n = a^n * b^n). These rules are crucial for simplifying expressions with multiple exponents.
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Simplification of Expressions
Simplification involves rewriting an expression in a more manageable or standard form. This often includes combining like terms, reducing fractions, and applying exponent rules. In the context of rational exponents, simplification may involve converting fractional exponents back to radical form or vice versa, making it easier to evaluate or compare expressions.
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