# 3.1 Exponents and roots

 Page 1 / 2
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 ${y}^{x}$ key to determine a root.

## Section overview

• Exponential Notation
• Reading Exponential Notation
• Roots
• Reading Root Notation
• Calculators

## Exponential notation

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

$8\cdot 8\cdot 8\cdot 8\cdot 8$

## Exponent

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, ${8}^{5}$ , in this case. The superscript is called an exponent .

## The function of an exponent

An exponent records the number of identical factors that are repeated in a multiplication.

## Sample set a

Write the following multiplication using exponents.

$3\cdot 3$ . Since the factor 3 appears 2 times, we record this as

${3}^{2}$

$\text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}\cdot \text{62}$ . Since the factor 62 appears 9 times, we record this as

${\text{62}}^{9}$

Expand (write without exponents) each number.

${\text{12}}^{4}$ . The exponent 4 is recording 4 factors of 12 in a multiplication. Thus,

${\text{12}}^{4}=\text{12}\cdot \text{12}\cdot \text{12}\cdot \text{12}$

${\text{706}}^{3}$ . The exponent 3 is recording 3 factors of 706 in a multiplication. Thus,

${\text{706}}^{3}=\text{706}\cdot \text{706}\cdot \text{706}$

## Practice set a

Write the following using exponents.

$\text{37}\cdot \text{37}$

${\text{37}}^{2}$

$\text{16}\cdot \text{16}\cdot \text{16}\cdot \text{16}\cdot \text{16}$

${\text{16}}^{5}$

$9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9$

${9}^{\text{10}}$

Write each number without exponents.

${\text{85}}^{3}$

$\text{85}\cdot \text{85}\cdot \text{85}$

${4}^{7}$

$4\cdot 4\cdot 4\cdot 4\cdot 4\cdot 4\cdot 4$

$1,{\text{739}}^{2}$

$1,\text{739}\cdot 1,\text{739}$

## Reading exponential notation

In a number such as ${8}^{5}$ ,

## Base

8 is called the base .

## Exponent, power

5 is called the exponent , or power . ${8}^{5}$ is read as "eight to the fifth power," or more simply as "eight to the fifth," or "the fifth power of eight."

## Squared

When a whole number is raised to the second power, it is said to be squared . The number ${5}^{2}$ can be read as

5 to the second power, or
5 to the second, or
5 squared.

## Cubed

When a whole number is raised to the third power, it is said to be cubed . The number ${5}^{3}$ can be read as

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 ${5}^{8}$ can be read as

5 to the eighth power, or just
5 to the eighth.

## Roots

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.

## Square root

We know that $\text{49}={7}^{2}$ , that is, $\text{49}=7\cdot 7$ . Through repeated multiplication, 7 is the source of 49. Thus, 7 is a root of 49. Since two 7's must be multiplied together to produce 49, the 7 is called the second or square root of 49.

## Cube root

We know that $8={2}^{3}$ , that is, $8=2\cdot 2\cdot 2$ . Through repeated multiplication, 2 is the source of 8. Thus, 2 is a root of 8. Since three 2's must be multiplied together to produce 8, 2 is called the third or cube root of 8.

#### Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
In the number 779,844,205 how many ten millions are there?
TELLY Reply
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
Khizar Reply
7hours 36 min - 4hours 50 min
Tanis Reply

### Read also:

#### Get Jobilize Job Search Mobile App in your pocket Now!

Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications? By OpenStax By Rohini Ajay By Rhodes By OpenStax By By OpenStax By Anh Dao By Saylor Foundation By Edward Biton By Madison Christian