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LovingMyself
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hi
LovingMyself
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whats the question
wild
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\[(3x)^-1 \over 4\]
wild
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write each expression so that it contains only positive exponents
LovingMyself
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I dunno this 1 im so sorry
anonymous
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\[\frac{(3x)^{-1}}{ 4}=\frac{1}{4(3x)}\]
wild
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how did you do that
anonymous
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\(b^{-1}=\frac{1}{b}\)
anonymous
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in general,
\[b^{-n}=\frac{1}{b^n}\]
wild
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how did you get b
anonymous
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i picked \(b\) as a variable
you can use anyone you prefer
wild
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oh ok
wild
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satellite are you there:(
Grazes
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I don't know what else there is to say. What don't you understand?
wild
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idk i just dont know how to do it
wild
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what happened to the -1
Grazes
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This is what your problem looks like, right?
\[\frac{ (3x)^{-1} }{ 4 }\]
Grazes
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This is what your problem looks like, right?
\[\frac{ (3x)^{-1} }{ 4 }\]
wild
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yes
Grazes
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Did you know that \[x^{-1}=\frac{ 1 }{ x }\]?
wild
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no
wild
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i thought x-1=1/x1
Grazes
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Same thing. \[x^1=x\] just like \[3^{1}=3\]
wild
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ok
wild
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but isnt negative 1
Grazes
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One thing first. Whenever you want to say that x has an exponential value of -1, you should type x^-1 or x to the power of -1 rather than x-1 because x-1 is just subtraction.
wild
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oh ok sorry
Grazes
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Is this what you're saying?\[x^{-1}=\frac{ 1 }{ x^{1} }\]
wild
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yes
Grazes
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Then you are right. But, as I said, \[x^{1}=x\]
So you can just change the \[x^{1}\] to \[x\]
wild
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oh ok
Grazes
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This means that \[x^{−1}=\frac{ 1 }{ x }\]
wild
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yeah i know
Grazes
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Rewrite this so that there are only positive exponents:\[\frac{ 1 }{ x^{-1} }\]
wild
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uh \[1\over x\]
wild
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i think
wild
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am i right
Grazes
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No. General rule of thumb. If you see a negative number as an exponent, flip the term(with the exponent) over the fraction bar and make the exponent positive
wild
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?
Grazes
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so I flip x^-1 over to the numerator and get \[x^{-1}\]
then I take away the negative sign which gets me \[x^{1}\] or \[x\]
wild
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so every time there an equation like this \[1 \over x ^-1\] you have to flip
Grazes
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Yes. But ONLY if the exponent is negative. Next problem:\[\frac{ 1 }{ x^{-2} }\]
wild
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so I fliped x^21 over to the numerator and get
x−2
then I take away the negative sign which gets me
x2
wild
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-2
Grazes
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x^2 is right. Next one:\[x ^{-3}\]
wild
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\[1\over x^2\]
Grazes
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Are you sure?
Grazes
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I think it's a silly mistake, but it was x^3, not x^2
Grazes
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Might be because the number was so small.
wild
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oh yeah it was a little as i looked closer it was a 3
wild
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\[1 \over x^3\]
Grazes
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Next one(and the important one to help you with your problem):\[\frac{ 4 }{ x^{-2} }\]
wild
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idk 4/x^2
Grazes
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Why don't you bring x^-2 to the numerator and take away the negative sign?
wild
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so it would be 4x^2
Grazes
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Exactly. Now can you do this?\[\frac{ (3x)^{-1} }{ 4 }\]
Grazes
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If you really don't understand, no is a good answer too.
wild
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im still thinking
wild
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3x/4
wild
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i got it wrong
Grazes
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Then change it :P
wild
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change what
Grazes
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remember what we did with \[x^{-2}\]
wild
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1/x^2
Grazes
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We flipped it into the denominator and took away the negative sign to get \[\frac{ 1 }{ x^{2} }\]
Grazes
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Can you apply this to your problem or should I just explain?
wild
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but 3 is a numerator too it can turn to 1
wild
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yeah you should explain i get everything you taught me i just can put it all together
Grazes
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Do you agree that \[(3x)^{-1}=\frac{ 1 }{ (3x)^{1} }\]or \[\frac{ 1 }{ (3x) }\]
wild
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\[1\over (3x)^1\]
Grazes
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Errr I mean that it equals both but the lower one without the exponent of 1 is simplified
Grazes
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But you agree with it, right?
wild
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yes
wild
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i should've looked at it as a whole
Grazes
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Now do you agree that \[(3x)^{−1}\times \frac{ 1 }{ 4 }=\frac{ (3x)^{−1} }{ 4 }\]
wild
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yes
Grazes
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so if you substitute the (3x)^-1 with \[\frac{ 1 }{ 3x}\] in the expression, you get \[\frac{ 1 }{ 4(3x) }\]
Grazes
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and that simplifies to\[\frac{ 1 }{ 12x }\]
Grazes
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But if you think about it, all I actually did was flip the (3x)^-1 over to the denominator and take away the negative sign|dw:1363833108473:dw|
wild
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is it the same thing as multiplying 1/3x and 1/4
Grazes
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Yes, but the point is that I just flipped it over and that it's incredibly simple.
Grazes
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Everyone else does it like:|dw:1363833370136:dw|
wild
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you know what your right its really easy well thank you very much i truly get thank you very much you should be a teacher and again thank you very much 100x:)
Grazes
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lolwut. Just understand it. and REMEMBER IT.
wild
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yes sir
wild
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lol
wild
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hahahadont make me take out my shoe