[<< 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!