Download Definition of Exponents: a is a real number, n is a natural number

Name: _________________________________
Date: ____________________
Period: ______
Properties of Exponents (Exponent is a Whole Number) Notes
Warm-Up
What is an exponent
represent? Explain in your own
words. You may show an
example to help you explain.
Definition of Exponents: a is a real number, n is a natural number
a n  a  a  a  ...  a, n times.
Properties of Exponents: Let a and b be nonzero real numbers. Let m and n be
integers.
Zero Exponent:
a0  1
Negative Exponent:
an 
Product:
a a
Quotient:
am
 a mn
an
Power of a Power:
a 
 a mn
Power of a Product:
 ab 
 a nb n
Power of a Quotient:
an
a

 
bn
b
m
Steps/Reminders
*Always look for zero
exponents first. You can turn
these to 1 and then simplify
further as needed.
*When doing power of a
product or power of a
quotient, do not forget to
apply the power to any
coefficients as well to all
variables.
*If there is a negative
exponent in your answer, then
you are not done. Make sure
you have flipped all negative
exponents.
m n
n
1
an
n
 a mn
n
Examples: Use your calculator to solve the following problems.
1.
 3  2 
5 2
 105 
2.  8 
 10 
1
Definition: A number is expressed in scientific notation if it is in the form c x
10n where 1  c < 10 and n is an integer.
(Example: 3.6 x 105 =36,000 or 8.13 x10-3=0.00813)
(Not Examples: 12.6 x10-2 or 0.4 x106)
Examples: Solve each of the following Scientific Notation problems.
4.32 x103
3.  4.05 103  3.325 106 
4.
6.3x107
Examples: Simplify and write with positive exponents.
z9
5. 3
6. k 3 k 5 k 8
z
7. 9a b  2a b
2 3
 3b 2 c 5 
8.  2 7 
 cb 

5 3 2
10.  x5 y 3 
9. x 4 x 2
 4a b 
12.  1 2 
 a b 
3 3
2
3
6
11.
  a 5 xy bc 2 x 1 

13. 
  a x b 4 y c 1 2 y 


0
Ticket out the Door
What is the hardest thing for you when you are solving these types of problems?
9 s 5t 4
3t 4