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Published byRoderick Marshall Modified over 7 years ago
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The Laws of Raising a Power to a Power & Negative exponents
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Raising a Power to a Power
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What does this expression really mean?
(53)2
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What does this expression really mean?
(53)2 53 ∙ 53
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What does this expression really mean?
(53)2 53 ∙ 53 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5
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What does this expression really mean?
(53)2 53 ∙ 53 = 56 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5
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What does this expression really mean?
(53)2 = 56 53 ∙ 53 = 56 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5
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Let’s look at another example.
(32)4
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Let’s look at another example.
(32)4 32 ∙ 32 ∙ 32 ∙ 32
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Let’s look at another example.
(32)4 32 ∙ 32 ∙ 32 ∙ 32 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3
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Let’s look at another example.
(32)4 32 ∙ 32 ∙ 32 ∙ 32 = 38 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3
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Let’s look at another example.
(32)4 = 38 32 ∙ 32 ∙ 32 ∙ 32 = 38 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3
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From these 2 examples, we can draw a conclusion.
(53)2 = 56 (32)4 = 38
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From these 2 examples, we can draw a conclusion.
3 ∙ 2 = 6 When raising an exponential expression to a power, simply keep the base and multiply the 2 exponents. (53)2 = 56 2 ∙ 4 = 8 (32)4 = 38
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Law of Raising a Power to a Power
(47 )3 = 47∙3 = 421 (33)4 = 33∙4 = 312 You try it! (2111)0 = (56)4
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Practice Time
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Simplify each expression.
10) (43)2 = 11) (82)4 = 12) (105)3 = 13) (c3)0 = 14) (r7)3 =
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Simplify each expression.
10) (43)2 = ) (82)4 = 12) (105)3 = 13) (c3)0 = 14) (r7)3 =
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Simplify each expression.
10) (43)2 = ) (82)4 = ) (105)3 = 13) (c3)0 = 14) (r7)3 =
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Simplify each expression.
10) (43)2 = ) (82)4 = ) (105)3 = ) (c3)0 = 14) (r7)3 =
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Simplify each expression.
10) (43)2 = ) (82)4 = ) (105)3 = ) (c3)0 = c0 or 1 14) (r7)3 =
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Simplify each expression.
10) (43)2 = ) (82)4 = ) (105)3 = ) (c3)0 = c0 or 1 14) (r7)3 = r21
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But what happens if you add or subtract the exponents and you get a negative number ?
First of all, there is no crying in math! Second, we have a law for that too! It’s called the Negative Rule! Let me tell you all about it…
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Negative Rule Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power. WHAT!! Click on this button to read more about it!
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…Negative Rule Remember that a reciprocal is the multiplicative inverse. In simple terms, flip the fraction! The reciprocal of is . If we apply the negative rule (Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power) then, A non-zero raised to a negative power = In this example, the negative in front of the four remains. Only the negative of the exponent is effected. The reciprocal raised to the opposite power
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Homework Worktext p. 109 (2-16)even
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