Laws of Exponents
Exponential Notation
BaseExponent
Base raised to an exponent
Goal
To write simplified statements that contain distinct bases, one whole number in the numerator and one in the denominator, and no negative exponents.
Ex:
21 4 3 8 4
2 122 1 2
9 9
46
a b b c
aa b c
Description of Lesson
This power point will address the laws of exponents in the following manner:
1. Explore how the rule works.
2. State the rule.
3. Provide an example with a solution.
4. Provide extra examples (Find me to get solutions)
Exploration
Evaluate the following without a calculator:
34 =
33 =
32 =
31 =
Describe a pattern and find the answer for:
30 =
81
27
9
3
1
÷ 3
÷ 3
÷ 3
÷ 3
Zero Power
Anything to the zero
power is oneCan “a” equal zero?
a0 = 1
No.
You can’t divide by 0.
xxxxxxx
7x
3 4x
Exploration
Simplify: x x3 4
Product of a Power
If you multiply powers having the same base, add the exponents.
m na
Example
Simplify:
32 9x
2 9 03x x y
113x
1
Practice
Simplify the following expressions:
5
3 0 2
3 5 2 4
1)
2) 2 3
3) 9 4
x x
x z x
x y x y
3 3 3 3 3x x x x x
15x
3 5x
Exploration
Simplify: 53x
Power of a Power
To find a power of a power, multiply the exponents.
m na
1 12 9 22 4s s t t
Example
Simplify: 6 32 3 22 4s s t t
13 118s t
2s 2 6s 3 3t 24t
2 4 1 12s 9 2t
Practice
Simplify the following expressions:
42
2 54 3
2 65 4 2
1)
2)
3)
y
a a
x y x x y
5x
2 2 2 2 2z x z x z x z x z x
5 10x z
Exploration
Simplify: 52z x
2 5z
Power of a Product
If a base has a product, raise each factor to the power
m ma b
20y
20y
2x 4 5y 23
Example
Simplify: 52 43 2x xy
7 20288x y
52 5x
2x9 32 5x2 5x 9 32
Practice
Simplify the following expressions:
5
4 52 3
32 4
1)
2) 2 2
3) - 2 3
pqr
ab a
x x yz
Negative Powers
A simplified expression has no negative exponents.
1ma
ma1ma
3b
3
620ba
6 320a b
Example
Simplify: 10 3 44 5a b a
4 5 10 4a
12
2 3128xy
Example
Simplify:2 1
3
12
8
x y
x
532xy
4
4
2x8
3x1y
Practice
Simplify the following expressions:
3
2
5 3
3 8 4
23
1) 8
62)
4
3) 3 y
4) 2
x
x y
x x
a b
x x x x x x x x x xx x x x x x
10 6x
Exploration
Simplify: 10
6xx
4x
Quotient of a Power
To find a quotient of a power, subtract
the bottom exponent from the top if the
bases are the same.
a0
m na
6 2x 26
4 213 x y
Example
Simplify:6
2 3
2
6
x y
x y
4
23xy
1 3y
1
Practice
Simplify the following expressions:6 0
3
6
12
9 3
3
1) 5
122)
4
143)
4
a b
a
x
xy
x y
x y
a a a a a ab b b b b b a a a a a ab b b b b b
Exploration
Simplify:6
a
b
6
6ab
To find a power of a quotient, raise the denominator and numerator to the same power.
Power of a Quotient
m
m
a
b
2y 5 3x 2 6 21
2 15
8
3
y x y
x
Example
Simplify:32 2 7
5
3 2x y
y x
2 6 21
15
8
9
y x y
x
2 3x 7 3y 3223
2 21
15 6
8
9
y
x
23
9
8
9
y
x
Practice
Simplify the following expressions:
2
83
0
4
2
75
4
1)
22)
3)
a
bc
x
y
s f
zr
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