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Chapter 2: Problem 329

In the following exercises, write in exponential form. $$ 2 \cdot 2 \cdot 2 $$

Short Answer

Expert verified
2^3

Step by step solution

01

Identify the Base

Determine the number that is being repeatedly multiplied. In this case, the base is 2.
02

Count the Number of Multiplications

Count how many times the base (2) is multiplied by itself. Here, 2 is multiplied 3 times.
03

Write in Exponential Form

Combine the base and the number of multiplications into an exponent. Therefore, the expression can be written as: 2^3

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Base in Exponentiation
Understanding the concept of the base in exponentiation is essential. In the expression given, you have repeated multiplication of the same number. This repeated number is known as the base. For instance, in the multiplication sequence \(2 \cdot 2 \cdot 2\), the number 2 is the base. The base is what you are multiplying by itself several times. Knowing the base helps identify the core element of the expression. In this case, our base is 2.
Counting Factors
Counting factors is an important step to convert a multiplication sequence into exponential form. In the previous example, \(2 \cdot 2 \cdot 2\), we need to count how many times the base (which is 2) appears in the multiplication. Each time you see the base, you count it. Here, you see that 2 is multiplied three times. So, the count of factors for 2 is 3. This count is called the exponent. It tells us how many times to multiply the base by itself. In this case, our exponent is 3.
Writing Exponents
After identifying the base and counting the factors, the final step is to write the expression in exponential form. The exponential form combines the base and the count of the factors using a small superscript. For example, from \(2 \cdot 2 \cdot 2\), we know the base is 2 and it appears 3 times. We write this as \(2^3\). The base is written as a regular number, and the exponent, which shows the number of multiplications, is written as a small number to the upper right of the base. This is the completed exponential form.

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