Transcript 7.3 Multiplication Properties of Exponents Pg. 460 Simplifying Exponential Expressions • There are No Negative Exponents • The same base does not appear more.

7.3 Multiplication Properties
of Exponents
Pg. 460
Simplifying Exponential Expressions
• There are No Negative Exponents
• The same base does not appear more than once
– In a Product or Quotient
•
•
•
•
No Powers are raised to Powers
No Products are raised to Powers
No Quotients are Raised to Powers
Numerical Coefficients in a quotient do not have
any common factor other than “1”
Examples
b
a
Non Examples
x3
5
4 4
ab
s
t5
2
a ba
z12
2
5a
2b
 ab 
4
xx
2
s
 
t
5
z 
3 4
10a 2
4b
Product of Powers Property
• The product of two powers with the
same base (Value or Variable) equals that
base raised to the sum of the exponents
– Rule
a a  a
n
m
 nm
• If they have the exact (same) base, add the
exponents
– REMEMBER
• Any constant or variable without an exponent, has
an exponent with the value of “1”
• EXAMPLES
 3 4 
3
4
7
x x  x
6 7  6 4  6
x
7  4
 611
Examples, product of powers
25  2 6 
2
4 3  4 3 
2
5
a b  a 
4
5
2
4
y  y y 
2
6
Scientific Notation Example
• Light from the sun travels at about 1.86 x 105 miles
per second. It takes about 500 seconds for the light
to reach the earth. Find the Distance from the Sun
to the Earth and write answer in Scientific Notation.
– We can not multiply as is
• We must change 500 to scientific Notation
• Then use the distance formula
Power of a Power Property
• A Power raised to another power equals that
base raised to the product of the exponents
– Rule
a 
m n
a
 m n 
• Remember that if no exponent is written the
exponent is “1”
• Example
6

7 4
 6 74  628
Examples, power of a power
7 
4 3
3 
6 0
x 
2 4
x
5
Examples, power of a product
 3x 
2
  3x 
x
2
y
2

0 3
7.4 Division Properties of
Exponents
Pg. 467
Quotient of Powers Property
Positive Power of a Quotient Property
Negative Power of a Quotient Property
Quotient of Powers Property
• The quotient of two non-zero powers with the
same base equals the base raised to the
difference of the exponents
• Rule
am
 mn
a
n
a
• Example
67
 7  4
3
6
6
4
6
Examples, quotient of powers
property
38
32
x5
x5
5 9
ab
 ab 
4
2 3 5
2  34  55
3
2
7
Dividing Scientific Notation
8
2
x
10
8
5
2
x
10

8
x
10

 
  8 x 105
Positive Powers of a Quotient
• A quotient raised to a positive power equals
the quotient of each base raised to that
power
• Examples
3
 
4
3
 2x 


yz


3
3
Negative Power of a Quotient
• A quotient raised to a negative power equals
the reciprocal of the quotient raised to the
opposite (positive) power
• Examples
2
 
5
3
 3x 
 2
y 
3
1
 3   2x 
   
 4   3y 
2
Homework
• 7.3 – 7.4 Book Problems
– Pg. 464, 18 – 52 Every Other Even
– Pg. 471, 18 – 44 Every Other Even
• Interim Review Due Tuesday