anonymous
  • anonymous
Express the following using inverse notation 1/(5x^3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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freckles
  • freckles
what do you mean by inverse notation?
imqwerty
  • imqwerty
do u mean like - 1/x = x^(-1)
freckles
  • freckles
\[y=\frac{1}{5x^3}\] I think you mean to write this maybe and you are looking for inverse function?

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freckles
  • freckles
I have no clue what you mean really
anonymous
  • anonymous
The problem says "Express the following in inverse notation"
freckles
  • freckles
You can please define that for me.
anonymous
  • anonymous
ill take a picture of it
1 Attachment
imqwerty
  • imqwerty
i think you are talking about multiplicative inverse? u in 6or7th grade?
anonymous
  • anonymous
Alright this is it
anonymous
  • anonymous
No Ive just been out of school for five years
freckles
  • freckles
\[\frac{1}{a}=a^{-1}\] @imqwerty made a great guess earlier
freckles
  • freckles
oh I don't know why that is called inverse notation in your class you are just writing the expression with negative exponents instead *
imqwerty
  • imqwerty
yea :D
anonymous
  • anonymous
So where is a good place to practice this because I really don't have a clue how you go the answer.
freckles
  • freckles
you see the exponent 3
freckles
  • freckles
on the bottom there?
anonymous
  • anonymous
yup
freckles
  • freckles
\[\frac{1}{5x^3}=\frac{1}{5} \frac{1}{x^3}=\frac{1}{5} x^{-3} \text{ use the rule I gave }\]
freckles
  • freckles
bring that little part to the numerator and change the sign of the exponent
anonymous
  • anonymous
That makes sense now.
freckles
  • freckles
another example: \[\frac{5}{3(x+1)} \\ \frac{5}{3} \frac{1}{x+1}=\frac{5}{3} \frac{1}{(x+1)^1} \\ =\frac{5}{3}(x+1)^{-1}\]
anonymous
  • anonymous
ah I see. This was easier than what I made it seem.
Rushwr
  • Rushwr
\[\frac{ 1 }{ 5x ^{3} } = y\] \[5y= \frac{ 1 }{ x ^{3} }\]
Rushwr
  • Rushwr
\[\sqrt[3]{5y} = x\]
imqwerty
  • imqwerty
hey is it like the minus sign of the exponent is not written or m getting something wrng.....this has happened to me before http://prntscr.com/8bpkrt
Rushwr
  • Rushwr
I have this link for you if u aren't sure of what you are doing ! https://www.mathsisfun.com/sets/function-inverse.html
anonymous
  • anonymous
|dw:1441192519704:dw|
anonymous
  • anonymous
Thanks @Rushwr
freckles
  • freckles
@milianbenja088321 I'm pretty certain "express the following using inverse notation" is not universal to mean \[\text{ to write } \frac{1}{a} \text{ as } a^{-1}\] just so you know
freckles
  • freckles
is this an american class?
anonymous
  • anonymous
@freckles yeah i figured as much thats why I was looking for a site to practice on.
anonymous
  • anonymous
@freckles its an entrance exam
freckles
  • freckles
most of the sites I can find go backwards they want positive exponents instead of negative exponents
freckles
  • freckles
http://www.purplemath.com/modules/exponent2.htm but you can read it from solution to problem and it is the same thing :p
anonymous
  • anonymous
@freckles its cool I appreciate all of your help. I will most certainly check the website out at this point anything will help.
freckles
  • freckles
for example in this link: \[(3x)^{-2}=\frac{(3x)^{-2}}{1}=\frac{1}{(3x)^2} \\ \text{ you can read this as } \\ \frac{1}{(3x)^2}=\frac{(3x)^{-2}}{1}=(3x)^{-2}\]
anonymous
  • anonymous
Thanks guys! I have to go. have a good day all!
freckles
  • freckles
you too
mathmate
  • mathmate
The "inverse" was meant to be the "multiplicative inverse" and not the inverse of a function. It gets confusing when the context is not clear.
freckles
  • freckles
@mathmate wouldn't the multiplicative inverse of \[\frac{1}{5x^3 } \text{ be } 5x^3 \text{ since } \frac{1}{5x^3} \cdot (5x^3)=1\] but they had \[\frac{1}{5}x^{-3}\] so to me the question still makes no sense
freckles
  • freckles
they should have said write with negative exponents
freckles
  • freckles
and I based this on their solutions
mathmate
  • mathmate
I do not disagree with the answer (1/5)x^-3 if the question was "Express the following using inverse notation" and not "Find the inverse of the following expression". Yes, I do find the question tricky, if not sneaky! :)
mathmate
  • mathmate
Context, context and context! At a particular grade, there is no confusion. Multiplicative inverse is probably the only one they have learned. I have seen questions asking for the inverse to mean negation, i.e. the additive inverse. It's the same as saying (in high school) "when the discriminant is negative, the quadratic equation has no root." It all depends on the context.
freckles
  • freckles
but \[\frac{1}{5}x^{-3} \text{ is \not the multiplicative inverse of } \frac{1}{5x^3}\]
freckles
  • freckles
oh I think I get what you are saying so why wouldn't the answer be: \[(5x^3)^{-1} \text{ instead }\]
mathmate
  • mathmate
They are asking to express the expression in inverse notation, not to find the inverse. So the value of the expression should stay the same, just the notation changes. This way we can safely say: 1/(5x^3) = (1/5)x^(-3). "Express the following with negative exponents" is clear for us, but probably does not achieve the purpose getting the students to learn the term "inverse". Just a guess!
freckles
  • freckles
but (5x^3)^(-1) is equivalent to the original expression and to me it is more an inverse notation because it actually obviously contains the multiplicative inverse inside the ( )^(-1)
mathmate
  • mathmate
Yes, I agree that (5x^3)^(-1) fits the concept of inverse even better. Some how I have the impression that the question is biased toward teaching the laws of exponents, so there! If I were to correct (manually), I would accept either option.
freckles
  • freckles
I still think the question would have been better phrased to just write with negative exponents. The answers to me our weird for inverse notation.
freckles
  • freckles
are weird*
mathmate
  • mathmate
Yes, I agree that "write with negative exponents" would be more suited for the "correct " answer.

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