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Published byAshlynn Barton Modified over 6 years ago

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Apply Properties of Multiplying Integer Exponents What if the chips represented 4 5 * 4 2 ? What would be a simplified expression? 4 4 4 4 44 4 X X X X X *

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Apply Properties of Multiplying Integer Exponents Using your chips, create an equivalent expression for: x 4 * x 2

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Apply Properties of Multiplying Integer Exponents What if the circles represented 4 5 * 4 -2 ?

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Apply Properties to Multiplying using Integer Exponents What is the new expression? Match positive and negative chips How could you rewrite this expression?

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Apply Properties to Multiplying using Integer Exponents What is the new expression?

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Apply Properties of Multiplying Integer Exponents 4 5 * 4 -2 = 4 5 * 1/4 2 = 4 3 44 4 4 4 4 4 X X X X X

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Apply Properties of Multiplying Integer Exponents Now use your chips for this problem: x 4 * x -2

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Apply Properties to Dividing using Integer Exponents What if the chips represented 4 6 / 4 2 ? Simplify by reducing to 1 4 4 4 4 4 X X X X 4 X 4 4 X

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Apply Properties to Dividing using Integer Exponents Now you have 1 * What is the simplified value?

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Apply Properties to Dividing using Integer Exponents What if the circles represented 4 6 / 4 -3 ? Simplify by reducing to 1 4 4 4 4 4 4 4 4 X X X X 4 X

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Apply Properties to Dividing using Integer Exponents What does 1/4 -3 mean? 4343

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Apply Properties to Dividing using Integer Exponents So, 4 6 / 4 -3 really means 4 6 * 4 3

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Apply Properties to Dividing using Integer Exponents What if the circles represented 4 6 / 4 6 ? = 1 Simplify to reduce to 1

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Apply Properties to Dividing using Integer Exponents What if the circles represented 4 6 / 4 6 ? Simplify to reduce to 1

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Apply Properties to Dividing using Integer Exponents Only thing left is… 1 So, a zero exponent means….

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Properties of Integer Exponents Positive exponents Multiplication of integer expressions Negative exponents Zero exponents Division of integer expressions

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Properties of Integer Exponents Positive exponents Ex: x 4 = x * x * x *x 5 2 = 5 * 5 = 25

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Properties of Integer Exponents Multiplying Integer exponents Equivalent to the base multiplied by itself the amount of the exponent x 2 * x 3 = x ? = 2 + 3 = 5 What is a quick way to find the exponent of the result?

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Properties of Integer Exponents Negative exponents Equivalent to the reciprocal of base to the positive exponent Ex: x -n = 1/x n 5 -2 = (1/5) 2 = 1/5 * 1/5 = 1/25 2

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Properties of Integer Exponents Dividing Integer Exponents Equivalent to the reciprocal of base to the positive exponent X 4 / x 2 = x ? 4 + (-2) = -2 What is a quick way to find the exponent of the result?

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Properties of Integer Exponents Zero exponents Equivalent to the value 1 Ex: x 0 = 1 5 0 = 1

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