Microsoft Power Point - Negative Exponents [Compatibility M

8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M

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Ne ative Ex onentsNe ative Ex onents

With Variable bases, regularWith Variable bases, regular

number bases and both.number bases and both.


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Negative ExponentsNegative Exponents

Definition:Definition: When you see a negative exponentWhen you see a negative exponent

immediately write down a fraction bar next to it.immediately write down a fraction bar next to it.Take the base that has a negative exponent andTake the base that has a negative exponent and

move it to the opposite portion on the fraction.move it to the opposite portion on the fraction.

After you make the move, the exponentAfter you make the move, the exponentbecomes positive.becomes positive.

Detail: If it is a whole number assume itDetail: If it is a whole number assume it

originates in the numerator and move it to theoriginates in the numerator and move it to thedenominator. If it is in the denominator move itdenominator. If it is in the denominator move it

to the numerator.to the numerator.


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EX 1EX 1

xx --33 ==

11 ==

yy --44


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Negative ExponentsNegative ExponentsEX 1EX 1

xx --33 ==

Ex 2Ex 2

S1) Write a fraction bar nextS1) Write a fraction bar next

to the problemto the problemS2) Put the base andS2) Put the base and

exponent in the oppositeexponent in the opposite

11 ==yy --44

(change the exponent to(change the exponent toa positive when you doa positive when you do

so.)so.)

* If nothing is left in the* If nothing is left in thenumerator, assume its anumerator, assume its a

_______._______.


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xx --33 == 11xx 33




Ex 2Ex 211 ==

yy --44


so.)so.)


___1____.___1____.


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xx --33 == 11xx 33




Ex 2Ex 211 == yy 44

yy --44


so.)so.)


___1____.___1____.


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Negative ExponentsNegative ExponentsEx 3Ex 3

3x3x --22 ==

Ex 4Ex 4

(3x)(3x) --22 ==


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3x3x --22 ==

EX 3EX 3

The exponent in this caseThe exponent in this casebelongs only to the variablebelongs only to the variablebefore it.before it. IT HAS NOTHINGIT HAS NOTHINGTO DO WITH THETO DO WITH THECOEFFICIENT!!COEFFICIENT!!

Ex 4Ex 4

(3x)(3x) --22 ==

EX 4EX 4

Because of the parenthesis,Because of the parenthesis,the base of this example isthe base of this example iseverything inside theeverything inside the

parenthesis. So we moveparenthesis. So we moveEVERYTHING inside theEVERYTHING inside theparenthesis.parenthesis.


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3x3x --22 == 33

xx 22

EX 3EX 3

The exponent in this caseThe exponent in this case

belongs only to the variablebelongs only to the variablebefore it.before it. IT HAS NOTHINGIT HAS NOTHINGTO DO WITH THETO DO WITH THECOEFFICIENT!!COEFFICIENT!!

Ex 4Ex 4

(3x)(3x) --22 ==

EX 4EX 4Because of the parenthesisBecause of the parenthesis,,the base of this example isthe base of this example iseverything inside theeverything inside theparenthesis. So we moveparenthesis. So we move

EVERYTHING inside theEVERYTHING inside theparenthesis. Then distributeparenthesis. Then distributethe exponent to each term.the exponent to each term.Inside the parenthesis.Inside the parenthesis.


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3x3x --22 == 33

xx 22

EX 3EX 3

The exponent in this caseThe exponent in this case

belongs only to the variablebelongs only to the variablebefore it.before it. IT HAS NOTHINGIT HAS NOTHINGTO DO WITH THETO DO WITH THECOEFFICIENT!!COEFFICIENT!!

Ex 4Ex 4

(3x)(3x) --22 == 11

9x9x 22

EX 4EX 4Because of the parenthesisBecause of the parenthesis,,the base of this example isthe base of this example iseverything inside theeverything inside theparenthesis. So we moveparenthesis. So we move

EVERYTHING inside theEVERYTHING inside theparenthesis. Then distributeparenthesis. Then distributethe exponent to each term.the exponent to each term.Inside the parenthesis.Inside the parenthesis.


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--5x5x--33

==yy --44

There are two differentThere are two differenttypes of negatives in Extypes of negatives in Ex5. A negative coefficient5. A negative coefficientis completely differentis completely differentthan a negative exponent.than a negative exponent.

Ex 6Ex 6

44 ==

aa --66

EXPONENTS MOVE.EXPONENTS MOVE.

Both of these regularBoth of these regularnumbers are going tonumbers are going tostay where they arestay where they areregardless of whetherregardless of whetherthey are negative or not!they are negative or not!


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--5x5x--33

== --5y5y44

yy --44 xx 33


Ex 6Ex 6

44 ==

aa --66




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--5x5x--33

== --5y5y44

yy --44 xx 33


Ex 6Ex 6

44 == 4a4a 66

aa --66




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44 --33

If you have a negativeIf you have a negative

exponent on aexponent on anumber, move thenumber, move the

number. Thennumber. Then

Ex 8Ex 8 11

33 --22

multiply using themultiply using theexponent.exponent.

Always multiply it out!!Always multiply it out!!


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44 --33 == 11 == 1144 33 6464




Ex 8Ex 8

1133 --22




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44 --33 == 11 == 1144 33 6464




Ex 8Ex 8

11 == 3322

== 9933 --22




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2 * 42 * 4 --22 ==

Key Point:Key Point:

The differenceThe differencebetween these twobetween these two

problems is ?problems is ?

Ex 10Ex 10 (2 * 4)(2 * 4) --22 ==

How does it changeHow does it change

the problem?the problem?


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2 * 42 * 4--22

==


The difference betweenThe difference betweenthese two problems isthese two problems is thethe

parenthesis.parenthesis.

(2 * 4)(2 * 4) --22 == How does it change theHow does it change the

problem?problem? The baseThe base in thein the

first problem is only 4, infirst problem is only 4, in

the second problem thethe second problem thebase is 2*4 or 8!base is 2*4 or 8! TheThe

answer changes a LOT!!answer changes a LOT!!


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2 * 42 * 4--22

== 22 == 22 == 1144 22 1616 88




(2 * 4)(2 * 4) --22 == How does it change theHow does it change the






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2 * 42 * 4--22

== 22 == 22 == 1144 22 1616 88




(2 * 4)(2 * 4) --22 == (8)(8)--22 == 11 == 11

88 22 6464

How does it change theHow does it change the






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Extra PracticeExtra Practice

1.1. 4x4x --33

2.2. (4x)(4x) --33

3.3. (2 * 5)(2 * 5) --22

4.4. 2 * 52 * 5 --22

Date post:	10-Apr-2018
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Microsoft Power Point - Negative Exponents [Compatibility M

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