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OBJECTIVE: The students will simplify expressions by using the laws of exponents.

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**3x3 2x2x2x2x2x2 10x10x10 5x5x5 1x1x1x1x1x1x1x1 Write in**

exponential form 3x3 2x2x2x2x2x2 10x10x10 5x5x5 1x1x1x1x1x1x1x1

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**HISTORY of the word EXPONENT.**

The term EXPONENT was introduced by Michael Stifel ( ) in 1544 in Arithmetica integra.

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**An exponent is simply shorthand for multiplying that number of identical factors.**

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**So 4³ is the same as (4)(4)(4), three identical factors of 4**

So 4³ is the same as (4)(4)(4), three identical factors of 4. And x³ is just three factors of x, (x)(x)(x).

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**Exponent is the power in an expression.**

13 7 Exponent BASE

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Exponents exponent power base

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Using the Calculator 5 4 Press 5 Press ^ Press 4 Then =

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**7 Laws of Exponents #1 PRODUCT LAW**

To Multiply LIKE Bases… …Copy the Base, Add Exponents

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**Product Law or Product Rule**

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**7 Laws of Exponents #2 QUOTIENT LAW**

To Divide LIKE Bases… …Subtract Exponents a4

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**Quotient Law or Quotient Rule:**

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**7 Laws of Exponents #3 EXPONENT of EXPONENT LAW**

To Raise a Power to a Power… …Multiply Exponents a12

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**Exponent of Exponent Law or Exponential Rule:**

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**7 Laws of Exponents #4 Raising a product to a power**

To Raise a QUANTITY to a Power, raise EACH Factor to that Power. (-3ab)2= 9a2b2

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**7 Laws of Exponents #5 Raising a quotient or a fraction to a power**

To Raise a FRACTION to a Power, raise BOTH Numerator & Denominator to that power. a4 b4

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**7 Laws of Exponents #6 NEGATIVE EXPONENT LAW**

Negative Exponents …Reciprocal with a Positive Exponent 1 ___ a3

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**#6: Negative Law of Exponents: If the base is powered by the**

negative exponent, then the base becomes reciprocal with the positive exponent.

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**Any nonzero number raised to the ZERO Power = ONE**

7 Laws of Exponents #7 Any nonzero number raised to the ZERO Power = ONE 1 1 1

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The Laws of Exponents: #7: Zero Law of Exponents: Any base powered by zero exponent equals one

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Basic Examples

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Basic Examples

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