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3.2 Exponent Laws
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December 04, 2013
3.2 Exponent Laws
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Lesson 3
Power Laws
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Example 1:
22 x 23
For the following examples write each product of powers as a single power. Then, evaluate the power.
What do you notice?
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What do you notice?
An Experiment
1. Choose a base2. Choose an exponent3. Multiply that power by the same base raised to a different exponent. What's the answer?
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Product Law
When multiplying powers with the same base, add the exponents to write the product as a single power.
(a)m × (a)n = (a)m+n
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Example 2: 43 x 45
Example 3: (-3)2 x (-3)3
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Example 4:
25 / 23
For the following examples write each quotient as a single power. Then, evaluate the power.
What do you notice?
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What do you notice?
An Experiment
1. Choose a base2. Choose an exponent3. Divide that power by the same base raised to a different exponent. What's the answer?
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Quotient Law
When dividing powers with the same base, subtract the exponents to write the quotient as a single power.
(a)m ÷ (a)n = am-n
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Example 5: 45 ÷ 42
Example 6: (-3)10 / (-3)7
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Assignment:
page 105-107 # 1, 5-13, 22
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Using the product or quotient law create an expression that equals 45
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More Exponent
Rules!
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Example 1:
(22)3
Write as expanded multiplication and then as a single power.
What do you notice?
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What do you notice?
An Experiment
1. Choose a base2. Choose an exponent3. Raise that to a more different exponent.
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Raising a Power to an Exponent(am)n = amn
When a power is raised to an exponent, multiply the exponents to write the expression with a single exponent.
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Write the following expressions as a single power, and then evaluate
a) (22)3
b) (33)2
c) [(3)4]3
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Raising a Product to an Exponent
(ab)m = ambm
When a product is raised to an exponent, you can rewrite each factor in the product with the same
exponent.
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Does it work?!
(4 × 2)3 = 43 ⋅ 23
Let's check if this works!
Method 1: Using order of operations:
Method 2: Using order of operations:
?
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Write the following expressions as the product of two powers, and then evaluate
a) (3(2))3
b) (5 x 4)4
c) [(3) x 7]2
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Raising a Quotient to an Exponent
b ≠ 0
When a quotient is raised to an exponent you can write each number in the quotient with the same exponent.
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Does it work?!
(4 ÷ 2)3 = 43 ÷ 23
Let's check if this works!
Method 1: Using order of operations:
Method 2: Using order of operations:
?
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Write the following expressions as the product of two powers, and then evaluate
a) (3 ÷ 2)3
b) (2 ÷ 5)5
c) [(3) ÷ 7]2
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