Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:11 minutes

Problem 15

Textbook Question

Simplify each expression. See Example 1. (9^3)(9^5)

Verified step by step guidance

Identify the expression: \((9^3)(9^5)\).

Recognize that the expression involves multiplying powers with the same base.

Apply the property of exponents: \(a^m \cdot a^n = a^{m+n}\).

Add the exponents: \(3 + 5\).

Rewrite the expression as a single power of 9: \(9^{3+5}\).

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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. One key property is that when multiplying two expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This property is essential for simplifying expressions like (9^3)(9^5).

Base and Exponent

In an expression of the form a^n, 'a' is called the base and 'n' is the exponent. The base indicates the number being multiplied, while the exponent shows how many times the base is used as a factor. Understanding the roles of base and exponent is crucial for simplifying expressions and performing calculations correctly.

Simplification of Expressions

Simplification involves rewriting an expression in a more concise or manageable form without changing its value. In the context of exponents, this often means applying exponent rules to combine terms. For instance, simplifying (9^3)(9^5) results in 9^(3+5) = 9^8, demonstrating how simplification can lead to clearer results.