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
Simplifying Radical Expressions
4:12 minutes
Problem 139
Textbook Question
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∜(g³h⁵/9r⁶)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radical Expressions
Radical expressions involve roots, such as square roots or fourth roots, which are used to express the principal root of a number or variable. In this case, the fourth root (∜) indicates that we are looking for a value that, when raised to the fourth power, gives the expression inside. Understanding how to manipulate and simplify radical expressions is crucial for solving problems involving roots.
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Exponents and Powers
Exponents represent repeated multiplication of a base number. In the expression g³h⁵/9r⁶, the exponents indicate how many times each variable is multiplied by itself. When simplifying expressions with exponents, it's important to apply the laws of exponents, such as the product of powers and the power of a power, to combine or reduce terms effectively.
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Simplifying Fractions
Simplifying fractions involves reducing the numerator and denominator to their lowest terms. This process often includes factoring out common factors and applying the properties of exponents. In the context of the given expression, simplifying the fraction g³h⁵/9r⁶ before taking the fourth root can make the operation more manageable and lead to a clearer final result.
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