Transcript Properties of Exponents Students will be able to use properties of exponents to evaluate and simplify expressions.

Properties of Exponents
Students will be able to use properties
of exponents to evaluate and simplify
expressions.
Exponent Properties - Multiplication
• There are two other properties of
exponents for multiplication:
• In all cases a and b stand for any real numbers,
m and n are any integers.
a 
m
 ab 
FHS
n
m
a
mn
m
a b
m
Pre-Algebra Review
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Exponent Properties - Multiplication
• Let’s look at an example that
demonstrates how
n
the second property a m  a mn works:

 
• We have the problem: a


2 3

• According to the property we should be able to
3
2
23
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find the answer this way: a
a a
 
• We know that a  a  a so this follows:
2
a 
2 3
 a  a   a  a   a  a   a
6
• Which gives us the same answer.
FHS
Pre-Algebra Review
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Exponent Properties - Multiplication
• Let’s look at an example that demonstrates how
m
the third property  ab   a mb m works:


• We have the problem:  a  b  
3
• According to the property we should be able to
3
find the answer this way:  ab   a 3b 3
• We know this:  ab    ab    ab    ab  
3
 a  a  a  b  b  b   a b
3
3
• Which gives us the same answer.
FHS
Pre-Algebra Review
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Exponent Property - Division
• There is one other property of exponents
for division:
• In all cases a and b stand for real
numbers, m and n are integers.
a 
 
b 
FHS
m
Pre-Algebra Review

a
m
b
m
, if b ≠ 0
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Exponent Properties - Division
• Let’s look at an example that demonstrates how
m
m

 works:
a
a
the second property  
   m 
b 
 b 
• According to the property we should be able to
find the answer this way:  a 3 a 3
   3
b
b 
• To write the problem in expanded form, we
3
would have:  a  3 a a a
a


b 

b

b

b

b
3
• Which gives us the same answer.
FHS
Pre-Algebra Review
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Examples of Exponent Properties
Simplify the following:
1.  x

2 3
 x6
4 2
12 3
2x
y

 8x y
2. 
3
4
2 x 

5.
4x 
4 3
3.  x y   3xy 
FHS
3
2 2
 9x 8 y 7
3
3
27x
 3x 
6. 

3

y
 xy 
2
2
x4

2
Pre-Algebra Review
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