1.1 Factors, products, and exponents

Overview

• Factors
• Exponential Notation

Factors

Let’s begin our review of arithmetic by recalling the meaning of multiplication for whole numbers (the counting numbers and zero).

Multiplication

In the addition

$7+7+7+7$

the number 7 is repeated as an addend* 4 times. Therefore, we say we have four times seven and describe it by writing

$4·7$

The raised dot between the numbers 4 and 7 indicates multiplication. The dot directs us to multiply the two numbers that it separates. In algebra, the dot is preferred over the symbol $\times$ to denote multiplication because the letter $x$ is often used to represent a number. Thus,

$4·7=7+7+7+7$

Factors and products

Exponential notation

Quite often, a particular number will be repeated as a factor in a multiplication. For example, in the multiplication

$7·7·7·7$

the number 7 is repeated as a factor 4 times. We describe this by writing $7^4.$ Thus,

$7·7·7·7=7^4$

The repeated factor is the lower number (the base), and the number recording how many times the factor is repeated is the higher number (the superscript). The superscript number is called an exponent.

Exponent

Sample set a

For Examples 1, 2, and 3, express each product using exponents.

Exercises

For the following problems, express each product using exponents.

For the following problems, expand each product (do not compute the actual value).

For the following problems, specify all the whole number factors of each number. For example, the complete set of whole number factors of 6 is 1, 2, 3, 6.