Properties of integer exponents edmodo 2012 13

Properties of Integer
Exponents

How do I simplify and evaluate
algebraic expressions involving
integer exponents?

How do I simplify and evaluate algebraic
expressions involving integer exponents?

Multiplication Property
• To multiply powers with the same
base, keep the base and add the
exponents m n m n
a a a
3 5 3 5 8
2 2 2 2


Add the

6 3 65 Exponents
6 3+5

6 8

(6 6 6) (6 6 6 6 6)



b 7 b 5 12
= b pull to the right
for answer

What can I do with this?

2 4
f h = ?


3
23 8 23 -5
=
Erase here for answer
23
r 8 r-5 = r3


It's your turn

c2 c5 = c7
move for answer


It's your turn!
6 -9 d-3
1. d = d move for answer

10
2. 7 7 = 7
2 8 move for answer

3. -8
16 16 = 16 -7 move for answer


Division Property
• To divide powers with the same
base, keep the base and subtract
m
the exponents
a m n
n
a
a
25
25 3
22
23


Division Property
Subtract the
Exponents
5
6 5 3
3
6
6 2
6 36
6 6 6 6 6 6 6
6 6 6 1


Division Property
It's your turn!
1. 2
5
2 23 2 1 2 3
2 3. 2 5. 22
23 25 22 2 5

25 8
4.
2 5 8 1 2 5
2 1
2. 2 2 6. 2
23 23 28 2 3
22


Raising a Power to a Power
• To raise a power to a power, keep
the base and multiply the exponents
m n
a am n

3 2
2 23 2
26


Raising a Power to a Power

(8 4)6 8 4 6 8 24
= =
3)-7 3 -7 -21 = 1
(8 = 8 = 8
821
-4)-5 420
(4 = 4-4 -5 =


Simplest Form

• Each base appears exactly once
• There are no negative exponents
• There are no powers of powers


Adding Exponential
Terms
• In order to add exponential terms, both
the base and the exponent must be the
same. Otherwise, they must be multiplied
out before they can be added.
• 72 + 72 = 2 x 72 = 2 x 49 = 98

• x2 + x2 = 2x2


Multiplying in Scientific
Notation
• Multiply the coefficients
• Use properties of exponents to
multiply the power of 10
• Simplify
4 x 103 • 3 x 104

12 x 107
1.2 x 108

Dividing in Scientific
Notation
• Divide the coefficients
• Use properties of exponents to
divide the power of 10
• Simplify
2 x 107 ÷ 4 x 104

.5 x 103
5 x 102

Practice
1. 2 x 107 • 4 x 104

2. 5 x 10-6 • 4 x 10-3

3. 3 x 10-3 • 4 x 104

4. 8 x 106 4 x 105

5. 6 x 103 3 x 10-6

6. 9 x 10-5 2 x 10-2

POD 4 Sep
• Today, the United States National Debt (how much we
owe) is projected to pass $16,000,000,000,000. The
number of taxpaying citizens in the U.S. population is a
little more than 100,000,000. If the debt is divided
equally among all taxpaying citizens, how much does
each taxpayer owe?
1. Represented in scientific notation
2. Represented in standard form


Multiplying/Dividing with
Integer Exponents
• Multiply/Divide the coefficients
• Use properties of exponents for the
variables
(2x2y3)(3xy-4)

4x4y6 ÷ 2x-2y8


Integer Exponents
(2x2y3)(3xy-4)


Integer Exponents
4x4y6 ÷ 2x-2y8


Properties of integer exponents edmodo 2012 13

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