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Chapter 1: Problem 9

Write exponential notation. $$ 2 \cdot n \cdot n \cdot n \cdot n $$

Short Answer

Expert verified
The exponential notation is \(2 \times n^4\).

Step by step solution

01

Identify the Base

Look at the repeated multiplication and identify the number or variable being multiplied. In this case, it is the variable 'n'.
02

Count the Factors

Count how many times 'n' is being multiplied by itself. Here, 'n' is multiplied a total of 4 times.
03

Write the Exponential Notation

Combine the base and the count of factors into exponential notation. The base 'n' raised to the power of 4 is written as \(n^4\). Therefore, the expression is written as: \(2 \times n^4\).

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Key Concepts

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

Base and Exponent
Understanding 'base and exponent' is crucial for working with exponential notation. The base is the number or variable that is being multiplied by itself. The exponent tells us how many times we multiply the base by itself. For example, in the expression \( n^4 \), 'n' is the base and 4 is the exponent. This means we multiply 'n' by itself four times. In our exercise, identifying 'n' as the base and counting how many times it appears helps us transform the repeated multiplication into a simpler exponential notation.
Multiplication
Multiplication allows us to combine numbers in an efficient way. Instead of adding the same number repeatedly, we can simply multiply. In the exercise given, we see repeated multiplication: \(2 \times n \times n \times n \times n\). Here, we are multiplying the number 2 and the variable 'n' multiple times. By recognizing these patterns, we can use exponential notation to simplify the expression.
Variable
A variable represents an unknown or changeable value. Common variables include letters like 'n', 'x', and 'y'. In our exercise, 'n' is a variable. Variables allow us to create general formulas and expressions. Think of them as placeholders that can take different values. In the expression \( 2 \times n \times n \times n \times n \), 'n' is multiplied by itself, demonstrating its role as a base in exponential notation. Instead of writing 'n' multiple times, we use 'n' raised to an exponent.

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