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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2:18 minutes

Problem 5

Textbook Question

Fill in the blank(s) to correctly complete each sentence. In the expression 6^3, 6 is the , and 3 is the .

Verified step by step guidance

Identify the structure of the expression \(6^3\).

Recognize that in an expression of the form \(a^b\), \(a\) is the base and \(b\) is the exponent.

Apply this understanding to the given expression \(6^3\).

Determine that 6 is the base of the expression.

Determine that 3 is the exponent of the expression.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Base

In an exponential expression, the base is the number that is being multiplied by itself. In the expression 6^3, the base is 6, which indicates that 6 will be used as a factor in the multiplication process. Understanding the role of the base is crucial for evaluating exponential expressions.

Exponent

The exponent in an exponential expression indicates how many times the base is multiplied by itself. In the expression 6^3, the exponent is 3, meaning that 6 is multiplied by itself three times (6 × 6 × 6). This concept is fundamental in understanding the growth of numbers in exponential form.

Exponential Notation

Exponential notation is a mathematical shorthand used to represent repeated multiplication of the same number. It consists of a base and an exponent, as seen in expressions like 6^3. This notation simplifies the writing and calculation of large numbers and is widely used in various mathematical applications.