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
Exponents
1:31 minutes
Problem 93d
Textbook Question
Textbook QuestionIn Exercises 91–100, simplify using properties of exponents. (20x^1/2)/(5x^1/4)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Exponents
The properties of exponents are rules that govern how to manipulate expressions involving powers. Key properties include the product of powers (a^m * a^n = a^(m+n)), the quotient of powers (a^m / a^n = a^(m-n)), and the power of a power ( (a^m)^n = a^(m*n)). Understanding these properties is essential for simplifying expressions with exponents.
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Simplifying Fractions
Simplifying fractions involves reducing them to their simplest form by dividing the numerator and denominator by their greatest common factor. In the context of exponents, this means applying the properties of exponents to both the coefficients and the variable parts of the fraction, allowing for a clearer and more manageable expression.
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Radicals and Rational Exponents
Radicals and rational exponents are closely related concepts in algebra. A square root can be expressed as a rational exponent, such that √x = x^(1/2). This relationship allows for the manipulation of expressions involving roots using the same exponent rules, facilitating the simplification of complex expressions that include both radicals and exponents.
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