logo
g Text Version
Beauty & Self
Books & Music
Career
Computers
Education
Family
Food & Wine
Health & Fitness
Hobbies & Crafts
Home & Garden
Money
News & Politics
Relationships
Religion & Spirituality
Sports
Travel & Culture
TV & Movies

dailyclick
Bored? Games!
Nutrition
Postcards
Take a Quiz
Rate My Photo

new
Painting
Heart Disease
Horror Literature
Dating
Hiking & Backpacking
SF/Fantasy Books
Healthy Foods


dailyclick
All times in EST

Full Schedule
g
g Math Site

BellaOnline's Math Editor

g

Exponent Basics


Can you remember when you learned multiplication and discovered multiplication was a faster and shorter way to represent repeated addition? Well there is a faster and shorter way to represent repeated multiplication such as 2 x 2 x 2 x2. It is called exponential notation or exponential form. So, 2 x 2 x 2 x2 can be represented as 2 ^4. The “2” is called the base, and the “4” is referred to as the exponent. The base tells you what number is repeatedly multiplied, and the exponent tells you how many times to multiply.

Before we work any problems, let’s look at how to read the exponential form.
3 --- > three to the first power
3^1 --- > three to the first power
3^2 --- > three to the second power or commonly called three squared
3^3 --- > three to the third power or sometimes referred to as three cubed
3^4 --- > three to the fourth power
3^5 --- > three to the fifth power
And so on.

Exponent Tip: Any number raised to the zero power is always one. For example, 4^0 = 1; 123^0 = 1

Let’s try a few problems. Write the exponential notation for the following expressions.

Example: 4 x 4 x 4 = 4^3

Practice I
Write the exponential notation for the following expressions.
a) 9 x 9 x 9 =
b) 10 x 10 x 10 x 10 =
c) (-3) x (-3) x (-3) x (-3) x (-3) =

Practice II
Solve.
Example: 2^4 = 2 x 2 x 2 x 2 = 16

Note: (-5)^2 is different from -5^2 (-5)^2 = (-5)(-5) = 25 However - 5^2 requires you to view the “-“ as a signal to find the opposite of the value. In other words cover up or ignore the “-“ for a moment and simplify 5^2 then restore the negative sign. Another way to remember: if the “-“ is within the parentheses, raise everything enclosed. Otherwise, the negative sign is excluded from the “activity of being raised to a power.” Thus, -5^2 = -25.

Solve:
a) 3^4 =
b) 5^3 =
c) 11^2 =
d) 6^4 =
e) (-4)^3 =
f) (-7)^2 =
g) 5^0 =
h) 1^3 =
i) - 2^4 =





Answers:

Practice I:
a) 9^3
b) 10^4
c) (-3)^5


Practice II:
a) 81
b) 125
c) 121
d) 1296
e) -64
f) 49
g) 1
h) 1
i) -16

More Exponent Talk – Basic Exponent Rules
Exponents are especially helpful when dealing with variables. Any letter can represent a variable. However, x and y are commonly used. For instance, a better way to represent “yyyy” is y^4. The important thing to remember is to only combine exponents that have the same base and to follow some basic exponent rules.

1. Product Rule: Multiplication
Let’s look at (x^4)(x^5)
= xxxx + xxxxx
= x^9
Add the Exponents

2. Quotient Rule: Division
(x^6) / (x^2)
= xxxxxx – xx
= x^4
Subtract the Exponents

3. Power raised to a Power
(mn)^2 = m^2 n^2

(m^4)^3 = m^12
Multiply the Exponents




Add Exponent+Basics to Twitter Add Exponent+Basics to Facebook Add Exponent+Basics to MySpace Add Exponent+Basics to Del.icio.us Digg Exponent+Basics Add Exponent+Basics to Yahoo My Web Add Exponent+Basics to Google Bookmarks Add Exponent+Basics to Stumbleupon Add Exponent+Basics to Reddit




Multiplication facts: Nines Timetables
How to Teach Math - Review
RSS
Related Articles
Editor's Picks Articles
Top Ten Articles
Previous Features
Site Map


For FREE email updates, subscribe to the Math Newsletter


Past Issues


print
Printer Friendly
bookmark
Bookmark
tell friend
Tell a Friend
forum
Forum
email
Email Editor


Content copyright © 2013 by Beverly Mackie. All rights reserved.
This content was written by Beverly Mackie. If you wish to use this content in any manner, you need written permission. Contact Beverly Mackie for details.

g


g features
Math MOOC - Free Online Math Courses - Self-Paced

Interactive App for Student Engagement

Free Teaching Math Videos for High School Teachers

Archives | Site Map

forum
Forum
email
Contact

Past Issues
memberscenter


vote
Poetry
Daily
Weekly
Monthly
Less than Monthly



BellaOnline on Facebook
g


| About BellaOnline | Privacy Policy | Advertising | Become an Editor |
Website copyright © 2013 Minerva WebWorks LLC. All rights reserved.


BellaOnline Editor