This document reviews the basic rules of exponents: 1) When multiplying terms with the same base, add the exponents 2) When dividing terms with the same base, subtract the exponents 3) When taking a power of a power, multiply the exponents It also explains that a negative exponent means to take the reciprocal and make the exponent positive. Finally, it provides some example expressions to simplify using these rules.

1. LET’S REVIEW
RULES OF EXPONENTS

2. REMEMBER
5
meansx x x x x x   

3. PRODUCT OF TERMS
2 4 6
2 4 6
means ( )( ) =
or
The shortcut is to add the exponents--
Be sure the base is the same.
x x x x x x x x x
x x
   


4. DIVISION OF TERMS
5
2
3
5 3 2
means
or
The shortcut is to just subtract the exponents
Again the bases must be the same.
x x x x x x
x
x x x x
x x
   

 


5. POWER OF A POWER
     
32 4 2 4 2 4 2 4 6 12
2 3 4 3 6 12
means
or
The shortcut is to multiply the exponents.
x y x y x y x y x y
x y x y 



6. NEGATIVE EXPONENTS
5
5
1
x
x
3
3
1
x
x


Remember a negative exponent means to move
the term up or down. Be sure you make the
exponent positive after you move it.

7. LET’S SIMPLIFY SOME EXPRESSIONS.
    
24 4 3
4
3 2
2 3
1. 3 2. 3 2
6
3. 4. 5
3
x y x y xy
x y
x y
x y



8. 8 2 5 4
2 2
2 3
1. 9 2. 6
2 5
3. 4.
x y x y
x y
y x
