Download M3 Section 11.1 Properties of Exponents Day 1

M3 Section 11.1 Properties of Exponents Day 1
Essential Question
How do you simplify expressions involving exponents?
Definition of Integer Exponents
Let a be a real number.
n
If n is a natural number, then a  a  a  a  ...  a , n
times.
Ex: 35 = 3  3  3  3  3 = 243
If a is nonzero, then a0 = 1. Ex: 50 = 1, (3x)0 = 1,
(anything but zero)0 = 1
If n is a natural number, then a =
-n
1
an
. Ex: 5
-2
1
1

= 52 25
A number is in scientific notation when it is in the form a x
10n where 1 < a < 10 and n is an integer.
1.
The volume of the planet Jupiter is 1.521 x 1015 km3.
a) Write this value in standard form.
b) If the volume of Venus is 9.868 x 1011 km3, how many
times larger is Jupiter than Venus?
Rational Exponents
For all positive real numbers a:
1
n
If n is a nonzero integer, then a  n a .
1
3
Ex: 27  3 27  3
If m and n are integers and n  0, then
a
m
n
m
 n1 
 a  
 
3
2
 
n
3
m
a
 21 
Ex: 36   36  



 n am .
36

3
 63  216
To type in calculator: 36 ^ (3/2)
Properties of Exponents
Let a and b be nonzero real numbers. Let
integers.
Product of Powers:
m and n be
a m a n  a m n
 a m
m n

a
Quotient of Powers:
 a n
Power of a Power:  a   a
n
n n
ab

a
b


Power of a Product:
m n
mn
n
n
a   a
Quotient of a Product:  
bn
b 
Examples
1. x4x5 =
3.
34  37
36
b)
3
 
4
Simplify each expression
a)
5.
(x4)5 =
Evaluate each expression
a)
4.
2.
(s t )
b)
4 7 3

2
Simplify 2z 3x
1
x 2y 5
(x 2 ) 4
5z  .
3
Write your answer with
positive exponents.
6.
2
Simplify 9a b
3
 2a b  .
5
3 2
Write your answer with
positive exponents.
7.
Write your answer with positive exponents.
3
 3b 2c 5 
Simplify  2 7  .
 c b 
8.
Write your answer with positive exponents.
3
 m 9n 
Simplify 
.
10 6 
 5m n 