View source for Algebra I/Content/Introduction to Basic Algebra Ideas/Exponents and Powers

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== Vocabulary ==
'''Exponent''' is a number written in superscript that denotes how many times the base will be multiplied by itself.
<br>'''Base''' is the number to be multiplied by itself.</br>
Example:
<br><math>5^2=25</math></br>

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

;3*3 = 3^2 
:Three times three equals three to the second power (or three squared)

;3*3*3 = 3^3 
:Three times three times three equals three to the third power (or three cubed)

;3*3*3*3= 3^4 
:Three times three times three times three equal three to the fourth power 
  
;2*2*2 = 2^3  
:Two times two times two equals two to the third power.

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

7^2
:Seven to the second power, or seven squared, means seven times seven.

7*7 
:Seven times seven is forty-nine.

49 
:So, seven to the second power equals forty-nine.

----

Area of a square = (length of the side) ^2
:The area, or space inside, of a square is equal to the length of the side of the square to the second power.

Area of a square with side length 3 meters
:If the square had a side length of 3 meters,
(3 meters)^2
:Then the area would be (3 meters) squared.
3*3 meters^2
:3 squared is the same as 3 times 3.
9 meters^2
:So, the area of a square with a side length of 3 meters is 9 meters squared.

----
c^2 where c=6
:First, we replace the variable "c" in the expression with 6, which is what it equals.
6^2 
:6 squared equals 6 times 6.
6*6 
:6 times 6 equals 36.
36
:So, c squared is 36.
----
x^3 where x = 10. 
:First, we replace the variable "x" in the expression with 10, which is what it equals.
10^3 
:10 to the third power, or 10 cubed, is equal to 10 times 10 times 10.
10*10*10
:10 times 10 equals 100.
100*10
:100 times 10 equals 1000.
1000
:So, x to the third power is 1000.
----
y^4 where y = 2
:First, we replace the variable "y" in the expression with 2, which is what it equals.
2^4
:2 to the fourth power is equal to 2 times 2 times 2 times 2.
2*2*2*2  
:2 times 2 equals 4.
4*2*2
:4 times 2 equals 8.
8*2
:And 8 times 2 equals 16.
16
:So, y to the fourth is 16.

== 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)

== Practice Problems ==
(Note: put answer in parentheses after each problem you write)

Evaluate the following expressions:

# 6^2 (36)
# 2^3 (8)
# 4^2 (16)
# 5^3 (125)
# 2^4 (16)
# 9^2 (81)
# 8^2 (64)

[[Category:Algebra]]