microsoft power point - negative exponents [compatibility m
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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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8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M
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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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Negative ExponentsNegative Exponents
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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Negative ExponentsNegative ExponentsEX 1EX 1
xx --33 == 11xx 33
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
Ex 2Ex 211 ==
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
___1____.___1____.
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Negative ExponentsNegative ExponentsEX 1EX 1
xx --33 == 11xx 33
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
Ex 2Ex 211 == yy 44
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
___1____.___1____.
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Negative ExponentsNegative ExponentsEx 3Ex 3
3x3x --22 ==
Ex 4Ex 4
(3x)(3x) --22 ==
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Negative ExponentsNegative ExponentsEx 3Ex 3
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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Negative ExponentsNegative ExponentsEx 3Ex 3
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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8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M
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Negative ExponentsNegative ExponentsEx 3Ex 3
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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8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M
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Negative ExponentsNegative ExponentsEx 5Ex 5
--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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8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M
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Negative ExponentsNegative ExponentsEx 5Ex 5
--5x5x--33
== --5y5y44
yy --44 xx 33
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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8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M
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Negative ExponentsNegative ExponentsEx 5Ex 5
--5x5x--33
== --5y5y44
yy --44 xx 33
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 == 4a4a 66
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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Negative ExponentsNegative ExponentsEx 7Ex 7
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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Negative ExponentsNegative ExponentsEx 7Ex 7
44 --33 == 11 == 1144 33 6464
If you have a negativeIf you have a negative
exponent on aexponent on anumber, move thenumber, move the
number. Thennumber. Then
Ex 8Ex 8
1133 --22
multiply using themultiply using theexponent.exponent.
Always multiply it out!!Always multiply it out!!
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8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M
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Negative ExponentsNegative ExponentsEx 7Ex 7
44 --33 == 11 == 1144 33 6464
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 == 3322
== 9933 --22
multiply using themultiply using theexponent.exponent.
Always multiply it out!!Always multiply it out!!
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8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M
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Negative ExponentsNegative ExponentsEx 9Ex 9
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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Negative ExponentsNegative ExponentsEx 9Ex 9
2 * 42 * 4--22
==
Key Point:Key Point:
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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8/8/2019 Microsoft Power Point - Negative Exponents [Compatibility M
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Negative ExponentsNegative ExponentsEx 9Ex 9
2 * 42 * 4--22
== 22 == 22 == 1144 22 1616 88
Key Point:Key Point:
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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Negative ExponentsNegative ExponentsEx 9Ex 9
2 * 42 * 4--22
== 22 == 22 == 1144 22 1616 88
Key Point:Key Point:
The difference betweenThe difference betweenthese two problems isthese two problems is thethe
parenthesis.parenthesis.
(2 * 4)(2 * 4) --22 == (8)(8)--22 == 11 == 11
88 22 6464
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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Negative ExponentsNegative Exponents
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
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