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EXPONENTS

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EXPONENTIAL NOTATION X IS THE BASE 2 IS THE EXPONENT OR POWER

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EXPONENTIAL NOTATION THE BASE IS SQUARED

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EXPONENTIAL NOTATION EXPONENT IS THE NUMBER OF TIMES THE BASE IS MULTIPLIED BY ITSELF

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EXPONENTIAL NOTATION Y IS THE BASE 8 IS THE EXPONENT

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EXPONENTIAL NOTATION Y IS THE BASE 8 IS THE EXPONENT

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Compare these two cases 6 IS THE BASE (THE NEG. SIGN IS NOT PART OF THE BASE, IT MUST REMAIN PART OF THE ANSWER) -6 IS THE BASE

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EXPONENTIAL NOTATION WHAT IS THE BASE? WHAT WILL BE SQUARED?

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EXPONENTIAL NOTATION WHAT IS THE BASE? -h is the base

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EXPONENTIAL NOTATION WHAT IS THE BASE? What will be raised to the 5th power?

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EXPONENTIAL NOTATION WHAT IS THE BASE? r will be raised to the 5th power

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TRY THESE

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EVALUATING EXPRESSIONS WITH EXPONENTS

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Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3

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Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3 1.Put in x & y values 2x 2 (x+y) = 2(6) 2 (6+3)

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Evaluating Expression with Exponents Evaluate 2x 2 (x+y) When x=6 & y=3 1.Put in x & y values 2.Use PEMDAS 2x 2 (x+y) = 2(6) 2 (6+3) = 2(6) 2 (9) = 2(36)9 = 729 = 648

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MULTIPLYING SIMILAR BASES X X2X2 X

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THE RULE IS TO ADD THE EXPONENTS

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MULTIPLYING SIMILAR BASES

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TRY THESE PROBLEMS

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DIVIDING SIMILAR BASES

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THE RULE IS TO SUBTRACT THE EXPONENT OF THE DENOMINATOR FROM THE EXPONENT OF THE NUMERATOR

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DIVIDING SIMILAR BASES THE RULE IS TO SUBTRACT THE EXPONENTS

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TRY THESE

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NEGATIVE EXPONENTS You can change a negative exponent to positive by switching it’s base from numerator to denominator or vice versa.

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NEGATIVE EXPONENTS MOVE THE BASE & EXPONENT FROM THE NUMERATOR TO THE DENOMINATOR OR VICE VERSA AND CHANGE THE SIGN OF THE EXPONENT

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NEGATIVE EXPONENTS X 2 /X 2 IS WHAT PROPERTY?

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MULTIPLY NUMERATORS & MULTIPLY DENOMINATORS NEGATIVE EXPONENTS

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ANYTHING TO THE ZERO POWER IS EQUAL TO ? NEGATIVE EXPONENTS

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Why is anything to the zero power equal to 1?

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Check Out These Patterns

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Or For Anything

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THIS IS WHY SWITCHING A NEGATIVE EXPONENT CHANGES ITS SIGN

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Let’s compare the Neg. Exponent Rule with the Dividing Fraction Rule To divide fractions you INVERT THE 2ND FRACTION AND CHANGE THE DIVISION SIGN TO MULTIPICATION For negative exponents you INVERT THE BASE WITH AND CHANGE THE SIGN OF THE EXPONENT

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Try These

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What if the negative exponent is in the denominator? The same rule of inverting the base with the exponent and making the exponent positive applies but let see why this is so.

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What if the negative exponent is in the denominator? Use the Multiplicative Identity to Simplify

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What if the negative exponent is in the denominator? Do you remember what x 0 is equal to?

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What if the negative exponent is in the denominator? INVERT AND CHANGE EXPONENT SIGN

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Try These

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Try These ANSWERS

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SUMMARY SO FAR DIVIDING EXPONENTS SUBTRACT THE EXPONENT OF THE DENOMINATOR FROM THE EXPONENT OF THE NUMERATOR MULTIPLYING EXPONENTS ADD THE EXPONENTS INVERTING A NEGATIVE EXPONENT CHANGES ITS SIGN

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DON’T BE MARY TO THE Z POWER GET WITH IT!

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POWER TO A POWER THIS IS A POWERFUL IDEA

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POWER TO A POWER VS. MULT. SIMILAR BASES

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POWER TO A POWER MULTIPLY THE EXPONENTS

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POWER TO A POWER Express Answers as Positive Exponents

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POWER TO A POWER

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COMPARING MULTIPLY SIMILAR BASES & POWER TO A POWER

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WHAT’S THE DIFFERENCE?

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NOTHING REALLY (A MONOMIAL IS A PRODUCT) A monomial is a term with a number and one or more variables (letters) raised to some power. Examples are:

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Let’s take a close look at DISTRIBUTING THE POWER

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Simplify (4d 5 ) 2 Power of a Monomial

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Simplify (4d 5 ) 2 = 4 12 d 52 = 4 2 d 10 1.Multiply the outside power to the inside powers. Power of a Monomial

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Simplify (4d 5 ) 2 = 4 12 d 52 = 4 2 d 10 = 16 d 10 1.Multiply the outside power to the inside powers. 2.Simplify Power of a Monomial

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Simplify (2x 3 y 4 ) 5 1.Multiply the outside power to the inside powers. 2.Simplify

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Power of a Monomial Simplify (2x 3 y 4 ) 5 = 2 15 x 35 y 45 = 2 5 x 15 y 20 or 32 x 15 y 20 1.Multiply the outside power to the inside powers. 2.Simplify

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Take a Power of a Quotient Simplify

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Take a Power of a Quotient Simplify 1.Multiply the outside power to the inside powers.

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Take a Power of a Quotient Simplify 1.Multiply the outside power to the inside powers. 2.Simplify

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Mult/Divide Monomials with Exponents

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1.Multiply the numbers 2.Multiply the Similar Variables by adding the exponents.

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Mult/Divide Monomials with Exponents 1.Multiply the numbers 2.Multiply the Similar Variables by adding the exponents. 3.Simplify

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5 Exponent Rules 1.When multiplying similar bases add exponents 2.When dividing similar bases subtract exponents 3.When inverting change exponents’ sign 4.When taking a power of a power multiply exponents 5.When taking a power of a product or quotient distribute the outside power to the inside powers

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DIVIDING EXPONENTS SUBTRACT THE EXPONENTS MULTIPLYING EXPONENTS ADD THE EXPONENTS Anything to the zero power equals 1 EXPONENTS (Or POWERS are REPEATED MULTIPICATION

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