Exam (elaborations) Mathematics

EXPONENT RULES & PRACTICE
1. PRODUCT RULE: To multiply when two bases are the same, write the base and ADD the exponents.

 ·
 

Examples:

A.   ·    B. 2 · 2  2 C.          

2. QUOTIENT RULE: To divide when two bases are the same, write the base and SUBTRACT the exponents.






Examples:

   
A.   B. 3 C.  
   


3. ZERO EXPONENT RULE: Any base (except 0) raised to the zero power is equal to one.

  
Examples:

A. 
 1 B. 6
 1 C. 7  
! 
 1

4. POWER RULE: To raise a power to another power, write the base and MULTIPLY the exponents.

  
·
Examples:

A.       B. 3   3 C. "    "



5. EXPANDED POWER RULE:




# 
 # $# %  # 
Examples:

A. 2   2 
8 
 '  (
)
*
C. $  %  )
 )
B. 6    6     36 
     
D. $ %        
+ ,


6. NEGATIVE EXPONENTS: If a factor in the numerator or denominator is moved across the fraction bar, the sign
of the exponent is changed.
 
 # 

 

-

 $# %  $
%
Examples:
 
A.      B. 4     C. /4     
 
    E. 3  /2    /6     
D. $  %  $  %   ,
0 - 1 1 2 ) 3 
   ) *
F.
2 -) 3 -4 0 G. /2     $ )
%  $

% 
)

CAUTION: / 5  For example: /3 5 
REMEMBER: An exponent applies to only the factor it is directly next to unless parentheses enclose other factors.
Examples:
A. /3  /3/3  9 B. /3  /9