[<< 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.
Base (or radix)
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!