Why can I not simplify $(y^6z^6)/x^6$ any further?
$begingroup$
There is something I am misunderstanding about simplification. For example:
Given: $y^6$$z^6$/$x^6$
Why can I not take the 6th roof of both to simplify to $yz$/$x$?
I clearly see that both expressions are not equal, yet I am tempted to make such a mistake. I realize that I cannot do this, perhaps someone can shed light on simplification rules. I realize this is a dumb question but I am revisiting math since I was never adept at it and I want to get good at it. My guess is that I am changing the value of it, and that simplifying is no longer taking place, I am not ordering everything into equal and less terms, I am changing the value. I get confused because it seems that I am just changing the proportions and not the value.
For context, I am reviewing exponent rules and here is a pic from the youtube video the problem is from: 
I understand the exponent rules, I just was tempted to attempt to simplify more at the end.
algebra-precalculus
edited Dec 22 '18 at 14:31
Larry
2,43331130
asked Dec 22 '18 at 3:49
SphygmomanometerSphygmomanometer
9810
$endgroup$
add a comment |
$begingroup$
There is something I am misunderstanding about simplification. For example:
Given: $y^6$$z^6$/$x^6$
Why can I not take the 6th roof of both to simplify to $yz$/$x$?
I clearly see that both expressions are not equal, yet I am tempted to make such a mistake. I realize that I cannot do this, perhaps someone can shed light on simplification rules. I realize this is a dumb question but I am revisiting math since I was never adept at it and I want to get good at it. My guess is that I am changing the value of it, and that simplifying is no longer taking place, I am not ordering everything into equal and less terms, I am changing the value. I get confused because it seems that I am just changing the proportions and not the value.
For context, I am reviewing exponent rules and here is a pic from the youtube video the problem is from:
I understand the exponent rules, I just was tempted to attempt to simplify more at the end.
algebra-precalculus
edited Dec 22 '18 at 14:31
Larry
2,43331130
asked Dec 22 '18 at 3:49
SphygmomanometerSphygmomanometer
9810
$endgroup$
6
$begingroup$
You may write it as $bigg(frac{yz}{x}bigg)^6$
$endgroup$
– Mason
Dec 22 '18 at 3:56
$begingroup$
The mistake that you're making is known by educators as the "Law of Universal Linearity". An entire thread on this topic can be found here. :-) math.stackexchange.com/questions/630339/…
$endgroup$
– John Joy
Dec 23 '18 at 14:22
add a comment |
$begingroup$
There is something I am misunderstanding about simplification. For example:
Given: $y^6$$z^6$/$x^6$
Why can I not take the 6th roof of both to simplify to $yz$/$x$?
I clearly see that both expressions are not equal, yet I am tempted to make such a mistake. I realize that I cannot do this, perhaps someone can shed light on simplification rules. I realize this is a dumb question but I am revisiting math since I was never adept at it and I want to get good at it. My guess is that I am changing the value of it, and that simplifying is no longer taking place, I am not ordering everything into equal and less terms, I am changing the value. I get confused because it seems that I am just changing the proportions and not the value.
For context, I am reviewing exponent rules and here is a pic from the youtube video the problem is from:
I understand the exponent rules, I just was tempted to attempt to simplify more at the end.
algebra-precalculus
edited Dec 22 '18 at 14:31
Larry
2,43331130
asked Dec 22 '18 at 3:49
SphygmomanometerSphygmomanometer
9810
$endgroup$
There is something I am misunderstanding about simplification. For example:
Given: $y^6$$z^6$/$x^6$
Why can I not take the 6th roof of both to simplify to $yz$/$x$?
I clearly see that both expressions are not equal, yet I am tempted to make such a mistake. I realize that I cannot do this, perhaps someone can shed light on simplification rules. I realize this is a dumb question but I am revisiting math since I was never adept at it and I want to get good at it. My guess is that I am changing the value of it, and that simplifying is no longer taking place, I am not ordering everything into equal and less terms, I am changing the value. I get confused because it seems that I am just changing the proportions and not the value.
For context, I am reviewing exponent rules and here is a pic from the youtube video the problem is from:
I understand the exponent rules, I just was tempted to attempt to simplify more at the end.
algebra-precalculus
algebra-precalculus
edited Dec 22 '18 at 14:31
Larry
2,43331130
asked Dec 22 '18 at 3:49
SphygmomanometerSphygmomanometer
9810
edited Dec 22 '18 at 14:31
Larry
2,43331130
asked Dec 22 '18 at 3:49
SphygmomanometerSphygmomanometer
9810
edited Dec 22 '18 at 14:31
Larry
2,43331130
edited Dec 22 '18 at 14:31
Larry
2,43331130
edited Dec 22 '18 at 14:31
Larry
2,43331130
2,43331130
asked Dec 22 '18 at 3:49
SphygmomanometerSphygmomanometer
9810
asked Dec 22 '18 at 3:49
SphygmomanometerSphygmomanometer
9810
asked Dec 22 '18 at 3:49
SphygmomanometerSphygmomanometer
9810
9810
6
$begingroup$
You may write it as $bigg(frac{yz}{x}bigg)^6$
$endgroup$
– Mason
Dec 22 '18 at 3:56
$begingroup$
The mistake that you're making is known by educators as the "Law of Universal Linearity". An entire thread on this topic can be found here. :-) math.stackexchange.com/questions/630339/…
$endgroup$
– John Joy
Dec 23 '18 at 14:22
add a comment |
6
$begingroup$
You may write it as $bigg(frac{yz}{x}bigg)^6$
$endgroup$
– Mason
Dec 22 '18 at 3:56
$begingroup$
The mistake that you're making is known by educators as the "Law of Universal Linearity". An entire thread on this topic can be found here. :-) math.stackexchange.com/questions/630339/…
$endgroup$
– John Joy
Dec 23 '18 at 14:22
6
6
$begingroup$
You may write it as $bigg(frac{yz}{x}bigg)^6$
$endgroup$
– Mason
Dec 22 '18 at 3:56
$begingroup$
You may write it as $bigg(frac{yz}{x}bigg)^6$
$endgroup$
– Mason
Dec 22 '18 at 3:56
$begingroup$
The mistake that you're making is known by educators as the "Law of Universal Linearity". An entire thread on this topic can be found here. :-) math.stackexchange.com/questions/630339/…
$endgroup$
– John Joy
Dec 23 '18 at 14:22
$begingroup$
The mistake that you're making is known by educators as the "Law of Universal Linearity". An entire thread on this topic can be found here. :-) math.stackexchange.com/questions/630339/…
$endgroup$
– John Joy
Dec 23 '18 at 14:22
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
You can only divide both sides by the same factor. For example, if you had $frac{6x}{6y}$, then you can divide both sides by $6$ and thus get $frac{x}{y}$.
But there is no such common factor in $frac {x^6}{y^6}$. The numerator has $6$ factors of $x$ ($x^6=x cdot x cdot x cdot x cdot x cdot x$) and the denominator has $6$ factors of $y$ ($y cdot y cdot y cdot y cdot y cdot y$)... meaning they have no common factors at all.
Compare:
$require{cancel}$
$$frac{6x}{6y}=frac{6 cdot x}{6 cdot y}=frac{cancel{6}cdot x}{cancel{6} cdot y}=frac{x}{y}$$
$$frac{x^6}{y^6}=frac{x cdot xcdot x cdot x cdot x cdot x}{y cdot y cdot y cdot y cdot y cdot y} text{ .... and there is nothing you can do}$$
answered Dec 22 '18 at 3:56
Bram28Bram28
63.2k44793
$endgroup$
$begingroup$
So given the $x^6/y^6$ ,Why couldn't I multiply the numerator and denominator by 1/6 and then be left with $x/y$?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 3:58
$begingroup$
@Sphygmomanometer you can, that is essentially what is done when you cancel the factor of 6.... as long as you multiply numerator and denominator by the same factor, you are OK
$endgroup$
– PhysicsMathsLove
Dec 22 '18 at 4:00
$begingroup$
@Sphygmomanometer You can .. but since neither side has a factor of $6$, nothing of interest would happen ... the one side only has a bunch of $x$'s, and the other side only has a bunch of $y$'s
$endgroup$
– Bram28
Dec 22 '18 at 4:00
$begingroup$
@PhysicsMathsLove so if that is allowed, is the proper simplified form $x/y$? (following Bram28 example)
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:04
2
$begingroup$
Ok I think I see my error, I am confusing simplifying with changing the value by performing operations on both numerator and denominator. So $x^6/y^6$ is already simplified to the fullest because there are no common factors that can be removed, by taking a root I am no longer in the business of simplifying, I am changing the value. Is this correct?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:10
|
show 6 more comments
$begingroup$
Sometimes, but not very often, things can be cancelled that should not be cancelled. It's true that $dfrac{19}{95}=dfrac 15$, but, that the $9$s cancel is just a happy coincidence.
It's a common temptation to want to cancel things that shouldn't be cancelled. For example
$dfrac{x+6}{y+6} ne dfrac xy$.
You should be looking up what cancelling is and how it works. The most common form of cancelling works because $1cdot x = x cdot 1 = x$. For example
$$dfrac{6x}{6y} = dfrac 66 cdot frac xy = 1 cdot dfrac xy = dfrac xy$$
In general, it just isn't true that $dfrac{x^6}{y^6}= dfrac xy cdot dfrac 66$. There are no laws of arithmetic that let you separate out the exponents like that.
answered Dec 22 '18 at 4:29
steven gregorysteven gregory
18.3k32258
$endgroup$
add a comment |
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2 Answers
2
active
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2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You can only divide both sides by the same factor. For example, if you had $frac{6x}{6y}$, then you can divide both sides by $6$ and thus get $frac{x}{y}$.
But there is no such common factor in $frac {x^6}{y^6}$. The numerator has $6$ factors of $x$ ($x^6=x cdot x cdot x cdot x cdot x cdot x$) and the denominator has $6$ factors of $y$ ($y cdot y cdot y cdot y cdot y cdot y$)... meaning they have no common factors at all.
Compare:
$require{cancel}$
$$frac{6x}{6y}=frac{6 cdot x}{6 cdot y}=frac{cancel{6}cdot x}{cancel{6} cdot y}=frac{x}{y}$$
$$frac{x^6}{y^6}=frac{x cdot xcdot x cdot x cdot x cdot x}{y cdot y cdot y cdot y cdot y cdot y} text{ .... and there is nothing you can do}$$
answered Dec 22 '18 at 3:56
Bram28Bram28
63.2k44793
$endgroup$
$begingroup$
So given the $x^6/y^6$ ,Why couldn't I multiply the numerator and denominator by 1/6 and then be left with $x/y$?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 3:58
$begingroup$
@Sphygmomanometer you can, that is essentially what is done when you cancel the factor of 6.... as long as you multiply numerator and denominator by the same factor, you are OK
$endgroup$
– PhysicsMathsLove
Dec 22 '18 at 4:00
$begingroup$
@Sphygmomanometer You can .. but since neither side has a factor of $6$, nothing of interest would happen ... the one side only has a bunch of $x$'s, and the other side only has a bunch of $y$'s
$endgroup$
– Bram28
Dec 22 '18 at 4:00
$begingroup$
@PhysicsMathsLove so if that is allowed, is the proper simplified form $x/y$? (following Bram28 example)
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:04
2
$begingroup$
Ok I think I see my error, I am confusing simplifying with changing the value by performing operations on both numerator and denominator. So $x^6/y^6$ is already simplified to the fullest because there are no common factors that can be removed, by taking a root I am no longer in the business of simplifying, I am changing the value. Is this correct?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:10
|
show 6 more comments
$begingroup$
You can only divide both sides by the same factor. For example, if you had $frac{6x}{6y}$, then you can divide both sides by $6$ and thus get $frac{x}{y}$.
But there is no such common factor in $frac {x^6}{y^6}$. The numerator has $6$ factors of $x$ ($x^6=x cdot x cdot x cdot x cdot x cdot x$) and the denominator has $6$ factors of $y$ ($y cdot y cdot y cdot y cdot y cdot y$)... meaning they have no common factors at all.
Compare:
$require{cancel}$
$$frac{6x}{6y}=frac{6 cdot x}{6 cdot y}=frac{cancel{6}cdot x}{cancel{6} cdot y}=frac{x}{y}$$
$$frac{x^6}{y^6}=frac{x cdot xcdot x cdot x cdot x cdot x}{y cdot y cdot y cdot y cdot y cdot y} text{ .... and there is nothing you can do}$$
answered Dec 22 '18 at 3:56
Bram28Bram28
63.2k44793
$endgroup$
$begingroup$
So given the $x^6/y^6$ ,Why couldn't I multiply the numerator and denominator by 1/6 and then be left with $x/y$?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 3:58
$begingroup$
@Sphygmomanometer you can, that is essentially what is done when you cancel the factor of 6.... as long as you multiply numerator and denominator by the same factor, you are OK
$endgroup$
– PhysicsMathsLove
Dec 22 '18 at 4:00
$begingroup$
@Sphygmomanometer You can .. but since neither side has a factor of $6$, nothing of interest would happen ... the one side only has a bunch of $x$'s, and the other side only has a bunch of $y$'s
$endgroup$
– Bram28
Dec 22 '18 at 4:00
$begingroup$
@PhysicsMathsLove so if that is allowed, is the proper simplified form $x/y$? (following Bram28 example)
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:04
2
$begingroup$
Ok I think I see my error, I am confusing simplifying with changing the value by performing operations on both numerator and denominator. So $x^6/y^6$ is already simplified to the fullest because there are no common factors that can be removed, by taking a root I am no longer in the business of simplifying, I am changing the value. Is this correct?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:10
|
show 6 more comments
$begingroup$
You can only divide both sides by the same factor. For example, if you had $frac{6x}{6y}$, then you can divide both sides by $6$ and thus get $frac{x}{y}$.
But there is no such common factor in $frac {x^6}{y^6}$. The numerator has $6$ factors of $x$ ($x^6=x cdot x cdot x cdot x cdot x cdot x$) and the denominator has $6$ factors of $y$ ($y cdot y cdot y cdot y cdot y cdot y$)... meaning they have no common factors at all.
Compare:
$require{cancel}$
$$frac{6x}{6y}=frac{6 cdot x}{6 cdot y}=frac{cancel{6}cdot x}{cancel{6} cdot y}=frac{x}{y}$$
$$frac{x^6}{y^6}=frac{x cdot xcdot x cdot x cdot x cdot x}{y cdot y cdot y cdot y cdot y cdot y} text{ .... and there is nothing you can do}$$
answered Dec 22 '18 at 3:56
Bram28Bram28
63.2k44793
$endgroup$
You can only divide both sides by the same factor. For example, if you had $frac{6x}{6y}$, then you can divide both sides by $6$ and thus get $frac{x}{y}$.
But there is no such common factor in $frac {x^6}{y^6}$. The numerator has $6$ factors of $x$ ($x^6=x cdot x cdot x cdot x cdot x cdot x$) and the denominator has $6$ factors of $y$ ($y cdot y cdot y cdot y cdot y cdot y$)... meaning they have no common factors at all.
Compare:
$require{cancel}$
$$frac{6x}{6y}=frac{6 cdot x}{6 cdot y}=frac{cancel{6}cdot x}{cancel{6} cdot y}=frac{x}{y}$$
$$frac{x^6}{y^6}=frac{x cdot xcdot x cdot x cdot x cdot x}{y cdot y cdot y cdot y cdot y cdot y} text{ .... and there is nothing you can do}$$
answered Dec 22 '18 at 3:56
Bram28Bram28
63.2k44793
edited Dec 22 '18 at 4:14
answered Dec 22 '18 at 3:56
Bram28Bram28
63.2k44793
answered Dec 22 '18 at 3:56
Bram28Bram28
63.2k44793
answered Dec 22 '18 at 3:56
Bram28Bram28
63.2k44793
63.2k44793
$begingroup$
So given the $x^6/y^6$ ,Why couldn't I multiply the numerator and denominator by 1/6 and then be left with $x/y$?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 3:58
$begingroup$
@Sphygmomanometer you can, that is essentially what is done when you cancel the factor of 6.... as long as you multiply numerator and denominator by the same factor, you are OK
$endgroup$
– PhysicsMathsLove
Dec 22 '18 at 4:00
$begingroup$
@Sphygmomanometer You can .. but since neither side has a factor of $6$, nothing of interest would happen ... the one side only has a bunch of $x$'s, and the other side only has a bunch of $y$'s
$endgroup$
– Bram28
Dec 22 '18 at 4:00
$begingroup$
@PhysicsMathsLove so if that is allowed, is the proper simplified form $x/y$? (following Bram28 example)
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:04
2
$begingroup$
Ok I think I see my error, I am confusing simplifying with changing the value by performing operations on both numerator and denominator. So $x^6/y^6$ is already simplified to the fullest because there are no common factors that can be removed, by taking a root I am no longer in the business of simplifying, I am changing the value. Is this correct?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:10
|
show 6 more comments
$begingroup$
So given the $x^6/y^6$ ,Why couldn't I multiply the numerator and denominator by 1/6 and then be left with $x/y$?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 3:58
$begingroup$
@Sphygmomanometer you can, that is essentially what is done when you cancel the factor of 6.... as long as you multiply numerator and denominator by the same factor, you are OK
$endgroup$
– PhysicsMathsLove
Dec 22 '18 at 4:00
$begingroup$
@Sphygmomanometer You can .. but since neither side has a factor of $6$, nothing of interest would happen ... the one side only has a bunch of $x$'s, and the other side only has a bunch of $y$'s
$endgroup$
– Bram28
Dec 22 '18 at 4:00
$begingroup$
@PhysicsMathsLove so if that is allowed, is the proper simplified form $x/y$? (following Bram28 example)
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:04
2
$begingroup$
Ok I think I see my error, I am confusing simplifying with changing the value by performing operations on both numerator and denominator. So $x^6/y^6$ is already simplified to the fullest because there are no common factors that can be removed, by taking a root I am no longer in the business of simplifying, I am changing the value. Is this correct?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:10
$begingroup$
So given the $x^6/y^6$ ,Why couldn't I multiply the numerator and denominator by 1/6 and then be left with $x/y$?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 3:58
$begingroup$
So given the $x^6/y^6$ ,Why couldn't I multiply the numerator and denominator by 1/6 and then be left with $x/y$?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 3:58
$begingroup$
@Sphygmomanometer you can, that is essentially what is done when you cancel the factor of 6.... as long as you multiply numerator and denominator by the same factor, you are OK
$endgroup$
– PhysicsMathsLove
Dec 22 '18 at 4:00
$begingroup$
@Sphygmomanometer you can, that is essentially what is done when you cancel the factor of 6.... as long as you multiply numerator and denominator by the same factor, you are OK
$endgroup$
– PhysicsMathsLove
Dec 22 '18 at 4:00
$begingroup$
@Sphygmomanometer You can .. but since neither side has a factor of $6$, nothing of interest would happen ... the one side only has a bunch of $x$'s, and the other side only has a bunch of $y$'s
$endgroup$
– Bram28
Dec 22 '18 at 4:00
$begingroup$
@Sphygmomanometer You can .. but since neither side has a factor of $6$, nothing of interest would happen ... the one side only has a bunch of $x$'s, and the other side only has a bunch of $y$'s
$endgroup$
– Bram28
Dec 22 '18 at 4:00
$begingroup$
@PhysicsMathsLove so if that is allowed, is the proper simplified form $x/y$? (following Bram28 example)
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:04
$begingroup$
@PhysicsMathsLove so if that is allowed, is the proper simplified form $x/y$? (following Bram28 example)
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:04
2
2
$begingroup$
Ok I think I see my error, I am confusing simplifying with changing the value by performing operations on both numerator and denominator. So $x^6/y^6$ is already simplified to the fullest because there are no common factors that can be removed, by taking a root I am no longer in the business of simplifying, I am changing the value. Is this correct?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:10
$begingroup$
Ok I think I see my error, I am confusing simplifying with changing the value by performing operations on both numerator and denominator. So $x^6/y^6$ is already simplified to the fullest because there are no common factors that can be removed, by taking a root I am no longer in the business of simplifying, I am changing the value. Is this correct?
$endgroup$
– Sphygmomanometer
Dec 22 '18 at 4:10
|
show 6 more comments
$begingroup$
Sometimes, but not very often, things can be cancelled that should not be cancelled. It's true that $dfrac{19}{95}=dfrac 15$, but, that the $9$s cancel is just a happy coincidence.
It's a common temptation to want to cancel things that shouldn't be cancelled. For example
$dfrac{x+6}{y+6} ne dfrac xy$.
You should be looking up what cancelling is and how it works. The most common form of cancelling works because $1cdot x = x cdot 1 = x$. For example
$$dfrac{6x}{6y} = dfrac 66 cdot frac xy = 1 cdot dfrac xy = dfrac xy$$
In general, it just isn't true that $dfrac{x^6}{y^6}= dfrac xy cdot dfrac 66$. There are no laws of arithmetic that let you separate out the exponents like that.
answered Dec 22 '18 at 4:29
steven gregorysteven gregory
18.3k32258
$endgroup$
add a comment |
$begingroup$
Sometimes, but not very often, things can be cancelled that should not be cancelled. It's true that $dfrac{19}{95}=dfrac 15$, but, that the $9$s cancel is just a happy coincidence.
It's a common temptation to want to cancel things that shouldn't be cancelled. For example
$dfrac{x+6}{y+6} ne dfrac xy$.
You should be looking up what cancelling is and how it works. The most common form of cancelling works because $1cdot x = x cdot 1 = x$. For example
$$dfrac{6x}{6y} = dfrac 66 cdot frac xy = 1 cdot dfrac xy = dfrac xy$$
In general, it just isn't true that $dfrac{x^6}{y^6}= dfrac xy cdot dfrac 66$. There are no laws of arithmetic that let you separate out the exponents like that.
answered Dec 22 '18 at 4:29
steven gregorysteven gregory
18.3k32258
$endgroup$
add a comment |
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Sometimes, but not very often, things can be cancelled that should not be cancelled. It's true that $dfrac{19}{95}=dfrac 15$, but, that the $9$s cancel is just a happy coincidence.
It's a common temptation to want to cancel things that shouldn't be cancelled. For example
$dfrac{x+6}{y+6} ne dfrac xy$.
You should be looking up what cancelling is and how it works. The most common form of cancelling works because $1cdot x = x cdot 1 = x$. For example
$$dfrac{6x}{6y} = dfrac 66 cdot frac xy = 1 cdot dfrac xy = dfrac xy$$
In general, it just isn't true that $dfrac{x^6}{y^6}= dfrac xy cdot dfrac 66$. There are no laws of arithmetic that let you separate out the exponents like that.
answered Dec 22 '18 at 4:29
steven gregorysteven gregory
18.3k32258
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Sometimes, but not very often, things can be cancelled that should not be cancelled. It's true that $dfrac{19}{95}=dfrac 15$, but, that the $9$s cancel is just a happy coincidence.
It's a common temptation to want to cancel things that shouldn't be cancelled. For example
$dfrac{x+6}{y+6} ne dfrac xy$.
You should be looking up what cancelling is and how it works. The most common form of cancelling works because $1cdot x = x cdot 1 = x$. For example
$$dfrac{6x}{6y} = dfrac 66 cdot frac xy = 1 cdot dfrac xy = dfrac xy$$
In general, it just isn't true that $dfrac{x^6}{y^6}= dfrac xy cdot dfrac 66$. There are no laws of arithmetic that let you separate out the exponents like that.
answered Dec 22 '18 at 4:29
steven gregorysteven gregory
18.3k32258
edited Dec 22 '18 at 5:48
answered Dec 22 '18 at 4:29
steven gregorysteven gregory
18.3k32258
answered Dec 22 '18 at 4:29
steven gregorysteven gregory
18.3k32258
answered Dec 22 '18 at 4:29
steven gregorysteven gregory
18.3k32258
18.3k32258
add a comment |
add a comment |
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You may write it as $bigg(frac{yz}{x}bigg)^6$
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– Mason
Dec 22 '18 at 3:56
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The mistake that you're making is known by educators as the "Law of Universal Linearity". An entire thread on this topic can be found here. :-) math.stackexchange.com/questions/630339/…
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– John Joy
Dec 23 '18 at 14:22