laws of exponents. exponential notation base exponent base raised to an exponent
TRANSCRIPT
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Laws of Exponents
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Exponential Notation
BaseExponent
Base raised to an exponent
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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
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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)
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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
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Zero Power
Anything to the zero
power is oneCan “a” equal zero?
a0 = 1
No.
You can’t divide by 0.
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xxxxxxx
7x
3 4x
Exploration
Simplify: x x3 4
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Product of a Power
If you multiply powers having the same base, add the exponents.
m na
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Example
Simplify:
32 9x
2 9 03x x y
113x
1
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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
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3 3 3 3 3x x x x x
15x
3 5x
Exploration
Simplify: 53x
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Power of a Power
To find a power of a power, multiply the exponents.
m na
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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
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Practice
Simplify the following expressions:
42
2 54 3
2 65 4 2
1)
2)
3)
y
a a
x y x x y
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5x
2 2 2 2 2z x z x z x z x z x
5 10x z
Exploration
Simplify: 52z x
2 5z
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Power of a Product
If a base has a product, raise each factor to the power
m ma b
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20y
20y
2x 4 5y 23
Example
Simplify: 52 43 2x xy
7 20288x y
52 5x
2x9 32 5x2 5x 9 32
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Practice
Simplify the following expressions:
5
4 52 3
32 4
1)
2) 2 2
3) - 2 3
pqr
ab a
x x yz
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Negative Powers
A simplified expression has no negative exponents.
1ma
ma1ma
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3b
3
620ba
6 320a b
Example
Simplify: 10 3 44 5a b a
4 5 10 4a
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12
2 3128xy
Example
Simplify:2 1
3
12
8
x y
x
532xy
4
4
2x8
3x1y
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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
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x x x x x x x x x xx x x x x x
10 6x
Exploration
Simplify: 10
6xx
4x
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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
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6 2x 26
4 213 x y
Example
Simplify:6
2 3
2
6
x y
x y
4
23xy
1 3y
1
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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
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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
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To find a power of a quotient, raise the denominator and numerator to the same power.
Power of a Quotient
m
m
a
b
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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
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Practice
Simplify the following expressions:
2
83
0
4
2
75
4
1)
22)
3)
a
bc
x
y
s f
zr