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Chapter 3: Problem 77

Write exponential notation for \(9 \cdot 9 \cdot 9 \cdot 9\).

Short Answer

Expert verified
\[ 9^4 \]

Step by step solution

01

Identify the Base

Determine the base number that is being multiplied repeatedly. In this case, the number 9 is multiplied multiple times.
02

Count the Number of Factors

Count how many times the base number (9) appears in the multiplication. Here, 9 is multiplied 4 times.
03

Write in Exponential Notation

Combine the base and the number of times it is multiplied into exponential notation. This is done by writing the base followed by an exponent indicating the number of times it is multiplied. So, the result is written as: \[ 9^4 \]

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Key Concepts

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

base number
When you see a multiplication problem involving the same number repeated multiple times, the number being multiplied is called the base number. In the exercise, the number 9 is the base number because it is the one being multiplied over and over. The base number is crucial as it sets the foundation of what you are repeatedly multiplying.
exponent
An exponent shows you how many times the base number is used as a factor in the multiplication. It is written as a smaller number to the upper right of the base number. For example, in the exponential notation \(9^4\), the number 4 is the exponent. This means 9 is multiplied by itself 4 times. Exponents make it easier to write and understand large multiplication problems.
multiplication
Multiplication is one of the basic arithmetic operations where you add a number to itself a certain number of times. In the context of exponential notation, multiplication involves multiplying the base number repeatedly based on the value of the exponent. For instance, in the problem \(9 \cdot 9 \cdot 9 \cdot 9\), multiplication is the process of taking the base number 9 and multiplying it by itself 4 times. Using exponential notation saves time and space and makes large multiplications easier to manage.

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Most popular questions from this chapter

Estimate each of the following by estimating each mixed numeral as a whole number or as a mixed numeral where the fraction part is \(\frac{1}{2}\) and by estimating each fraction as \(0, \frac{1}{2},\) or 1 . $$ 1 \frac{5}{8}+1 \frac{27}{28} \cdot 6 \frac{35}{74} $$

Simplify. $$ \left(\frac{2}{3}+\frac{3}{4}\right) \div\left(\frac{5}{6}-\frac{1}{3}\right) $$

Subtract and simplify. $$ \frac{11}{12}-\frac{2}{12} $$

Add and simplify. $$ \frac{8}{10}+\frac{7}{100}+\frac{4}{1000} $$

Simplify. $$ \frac{28}{\frac{7}{4}} $$
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