[<< wikibooks] Basic Algebra/Introduction to Basic Algebra Ideas/Exponents and Powers
== Vocabulary ==
Exponent
A number written in superscript that denotes how many times the base will be multiplied by itself.
The number to be multiplied by itself.Example:

5

2

=
25

{\displaystyle 5^{2}=25}

In this example, the base is 5 and the exponent is 2.

== Lesson ==
We use exponents to show when we're multiplying the same number more than one time.

3
×
3
=

3

2

{\displaystyle 3\times 3=3^{2}}

Three times three equals three to the second power (or three squared)

3
×
3
×
3
=

3

3

{\displaystyle 3\times 3\times 3=3^{3}}

Three times three times three equals three to the third power (or three cubed)

3
×
3
×
3
×
3
=

3

4

{\displaystyle 3\times 3\times 3\times 3=3^{4}}

Three times three times three times three equal three to the fourth power

2
×
2
×
2
=

2

3

{\displaystyle 2\times 2\times 2=2^{3}}

Two times two times two equals two to the third powerNote that any nonzero number raised to the 0 power is always equal to 1.

2

0

=
1

{\displaystyle 2^{0}=1}

Two to the zero power equals oneWe can also raise any number to a negative exponent.  This is called the inverse exponent and places the number on the bottom of a fraction with a 1 on top:

2

−
2

=

1

2

2

=

1
4

{\displaystyle 2^{-2}={\frac {1}{2^{2}}}={\frac {1}{4}}}

Two to the negative two equals one over two to the second power

== Example Problems ==
Let's evaluate these expressions.

7

2

{\displaystyle 7^{2}}
Seven to the second power equals forty-nine.
What is the area of a square with a side of 3 meters length?So, the area of a square with a side length of 3 meters is 9 square meters.

c

2

{\displaystyle c^{2}}
where

c
=
6

{\displaystyle c=6}
So, c squared is 36.

x

3

{\displaystyle x^{3}}
where

x
=
10

{\displaystyle x=10}
.So, x to the third power is 1000.

y

4

{\displaystyle y^{4}}
where

y
=
2

{\displaystyle y=2}
So, y to the fourth is 16.

3

−
3

{\displaystyle 3^{-3}}
So, three to the negative third power equals one twenty-seventh.

== Practice Games ==
http://www.math.com/school/subject2/practice/S2U2L2/S2U2L2Pract.html
http://www.quia.com/pop/50485.html (scientific notation)
http://www.softschools.com/math/games/exponents_practice.jsp
http://www.quia.com/quiz/358716.html (King Kong Scientific Notation)
http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/ (order of operations including exponents)

== Practice Problems ==
Use / as the fraction line!