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Chapter 2: Problem 31

Write in exponential form. 3\(\cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\)

Short Answer

Expert verified
3^7

Step by step solution

01

Identify the Base

Determine the repeated factor in the given multiplication. In this case, the factor being repeated is 3.
02

Count the Number of Times the Base is Repeated

Count how many times the base (3) is being multiplied by itself. Here, 3 is multiplied 7 times.
03

Write in Exponential Form

Combine the base and the exponent (the number of times the base is multiplied by itself) to write the expression in exponential form. The expression is written as \(3^7\).

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Key Concepts

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

Base in Exponentiation
Exponentiation involves two key parts: the base and the exponent. The base is the number that is being multiplied. In our exercise, the base is 3. Every time you see repeated multiplication like 3\(\cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\), the base stays the same. Knowing the base helps you simplify repeated multiplications into a single expression.
Counting Factors
When you see a repeated multiplication, count how many times the base appears. This count becomes the exponent in the exponential form. For instance, in the sequence 3 \(\cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\), 3 is repeated 7 times. So, the exponent is 7. If you only count six factors, it wouldn't represent the multiplication correctly. This step ensures the accuracy of your final exponential expression.
Writing Exponents
After determining the base and counting the factors, you can write the expression in exponential form. Combine the base and the exponent to form the exponential notation. In our example, since 3 is the base and it鈥檚 repeated 7 times, we write this as 3\(\^7\). This notation means 3 is multiplied by itself 7 times. Using exponential notation makes expressions compact and easier to read, especially when dealing with large numbers of factors.

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