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

1:23 minutes

Problem 14a

Textbook Question

Simplify each expression. See Example 1. (a^8)(a^5)(a)

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.

Properties of Exponents

The properties of exponents are rules that govern how to manipulate expressions involving powers. Key rules include the product of powers rule, which states that when multiplying like bases, you add the exponents (a^m * a^n = a^(m+n)). Understanding these properties is essential for simplifying expressions with exponents.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms and applying mathematical operations to reduce the expression to its simplest form. This process often requires the use of exponent rules, distribution, and factoring. Mastery of simplification is crucial for solving equations and performing algebraic manipulations.

Like Bases

Like bases refer to terms in an expression that have the same base but may have different exponents. For example, in the expression (a^8)(a^5)(a^1), all terms have the base 'a'. Recognizing like bases allows for the application of exponent rules, particularly the product of powers rule, to simplify the expression effectively.