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

College Algebra

0. Review of Algebra

Radical Expressions

1:12 minutes

Problem 107d

Textbook Question

In Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3

Verified Solution

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

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 cube roots. The index of a radical indicates the degree of the root; for example, in ⁹√x^6, the index is 9, meaning we are looking for the ninth root. Understanding how to manipulate these expressions is crucial for simplification.

Properties of Exponents

The properties of exponents govern how to simplify expressions involving powers. Key rules include the product of powers, quotient of powers, and power of a power. For instance, x^a * x^b = x^(a+b) and (x^a)^b = x^(a*b), which are essential for reducing the index of radicals.

Simplifying Radicals

Simplifying radicals involves expressing a radical in its simplest form, often by factoring out perfect powers. For example, to simplify ⁹√x^6 y^3, one would identify how many times the base can be divided by the index, allowing for the extraction of whole numbers from the radical. This process is key to solving problems involving radicals.