Problem 64 - Elementary Algebra

Question

Supply the missing word. An exponent records the number of identical in a multiplication.

Step-by-Step Solution

Answer

Answer: An exponent represents the number of identical factors in a multiplication.

Step 1: Understanding the role of exponents

Exponents are used to indicate how many times a base number, or the number being multiplied, is being multiplied by itself. The exponent tells you the number of identical factors in the multiplication.

Step 2: Identify the missing word

Based on the explanation in step 1, the missing word is "factors". The complete sentence is: An exponent records the number of identical factors in a multiplication.

Key Concepts

Base Number

In algebra, when we talk about exponents, we must first understand what a base number is. The base number is the number that is being multiplied by itself; it serves as the foundation for the multiplication process. For example, in the expression \( 3^4 \), the base number is 3. This means that we take the number 3 and multiply it by itself a number of times specified by the exponent, which in this case is 4.

Factors in Multiplication

Multiplication can be thought of as repeated addition, and when we are dealing with exponents, the repeated addition turns into repeated multiplication. A factor is a number that divides into another number without leaving a remainder. In the context of exponents, when we multiply the base number by itself, each iteration of the base is considered a factor in the multiplication. So, if we have \( 2^3 \), the number 2 is multiplied by itself three times, which means there are three factors of 2 in the multiplication: \( 2 \times 2 \times 2 \).

Identical Factors

Identical factors refer to the factors in a multiplication that are exactly the same. This concept is crucial when understanding exponents because an exponent communicates how many times a base number serves as an identical factor in the multiplication. For example, in \( 5^2 \), the base number 5 is used as an identical factor twice, resulting in the multiplication \( 5 \times 5 \). The exponent here is instructive, telling us that there are two identical factors of 5.