 Exponential Notation
 Reading Exponential Notation
 Roots
 Reading Root Notation
 Calculators
Summary:
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses exponents and roots. By the end of the module students should be able to understand and be able to read exponential notation, understand the concept of root and be able to read root notation, and use a calculator having the
We have noted that multiplication is a description of repeated addition. Exponential notation is a description of repeated multiplication.
Suppose we have the repeated multiplication
The factor 8 is repeated 5 times. Exponential notation uses a superscript for the number of times the factor is repeated. The superscript is placed on the repeated factor,
An exponent records the number of identical factors that are repeated in a multiplication.
Write the following multiplication using exponents.
Expand (write without exponents) each number.
Write the following using exponents.
Write each number without exponents.
In a number such as
8 is called the base.
5 is called the exponent, or power.
When a whole number is raised to the second power, it is said to be squared. The number
5 to the second power, or
5 to the second, or
5 squared.
When a whole number is raised to the third power, it is said to be cubed. The number
5 to the third power, or
5 to the third, or
5 cubed.
When a whole number is raised to the power of 4 or higher, we simply say that that number is raised to that particular power. The number
5 to the eighth power, or just
5 to the eighth.
In the English language, the word "root" can mean a source of something. In mathematical terms, the word "root" is used to indicate that one number is the source of another number through repeated multiplication.
We know that
We know that
We can continue this way to see such roots as fourth roots, fifth roots, sixth roots, and so on.
There is a symbol used to indicate roots of a number. It is called the radical sign
The symbol
We discuss particular roots using the radical sign as follows:
In an expression such as
5 is called the index. (The index describes the indicated root.)
32 is called the radicand.
Find each root.
Check:
Check:
Find the following roots using only a knowledge of multiplication.
8
10
4
2
Calculators with the
Use the calculator to find
Display Reads  
Type  121  121 
Press 

11 
Find
Display Reads  
Type  2187  2187 
Press 

2187 
Type  7  7 
Press 

.14285714 
Press  =  3 
Use a calculator to find the following roots.
9
54
231
4
For the following problems, write the expressions using exponential notation.
For the following problems, expand the terms. (Do not find the actual value.)
For the following problems, determine the value of each of the powers. Use a calculator to check each result.
For the following problems, find the roots (using your knowledge of multiplication). Use a calculator to check each result.
4
8
12
15
2
6
20
100
60
For the following problems, use a calculator with the keys
34
4,158
24
4
5
81
((Reference)) Use the numbers 3, 8, and 9 to illustrate the associative property of addition.
((Reference)) In the multiplication
8 is the multiplier; 4 is the multiplicand
((Reference)) Does the quotient
((Reference)) Does the quotient
Yes; 0
((Reference)) Use the numbers 4 and 7 to illustrate the commutative property of multiplication.
"Used as supplemental materials for developmental math courses."