Problem 6 Write exponential notation. $$... [FREE SOLUTION]

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Chapter 1: Problem 6

Write exponential notation. $$ (-7)(-7)(-7)(-7) $$

Short Answer

Expert verified

(-7)^4

Step by step solution

Identify the Base

The base is the number that is being repeatedly multiplied. In this case, the base is (-7).

Count the Number of Factors

Count how many times the base (-7) is being multiplied. Here, (-7) appears 4 times.

Write in Exponential Notation

Express the repeated multiplication using exponential notation. The base is (-7) and it is multiplied 4 times, so it is written as (-7)^4.

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Key Concepts

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

Base Number

In exponential notation, the *base number* is fundamental. It tells which number is being multiplied. Look at the series of multiplications you have. In our example, (-7)(-7)(-7)(-7), the base number is clearly (-7). You can think of the base as the anchor of the expression. It stays the same and doesn't change, while other parts, like the exponent, tell us more about how often it is used. Recognizing the base is crucial because it helps you understand what number is being worked with throughout the entire expression.

Repeated Multiplication

When we talk about *repeated multiplication*, it means multiplying the same number several times. Instead of writing (-7)(-7)(-7)(-7), we can simplify it using exponential notation. This makes the expression shorter and easier to manage. If you see the base (-7) four times, that's repeated multiplication. It might seem tedious to write it out in full, which is where exponential notation comes in handy. This way, you avoid repetition and convey the same mathematical concept more efficiently.

Exponent

*Exponent* is a key part of exponential notation. Once you've identified your base number and noticed how many times it's being multiplied, you use the exponent to show this in a compact form. In our example of (-7)(-7)(-7)(-7), the exponent is 4, because (-7) is multiplied four times. Exponential notation is then written as ewline \[\begin{equation} (-7)^4 ewline \end{equation}\]. The exponent tells you the number of times to multiply the base by itself. This makes understanding, writing, and working with large numbers or many multiplications much simpler. Remember, the base is the number you start with, and the exponent tells you how many times to use it in multiplication.

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91影视

Write exponential notation. $$ (-7)(-7)(-7)(-7) $$

Short Answer

Step by step solution

Identify the Base

Count the Number of Factors

Write in Exponential Notation

Key Concepts

Base Number

Repeated Multiplication

Exponent

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