Express the following using inverse notation
1/(5x^3)

- anonymous

Express the following using inverse notation
1/(5x^3)

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- freckles

what do you mean by inverse notation?

- imqwerty

do u mean like - 1/x = x^(-1)

- 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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## More answers

- freckles

I have no clue what you mean really

- anonymous

The problem says "Express the following in inverse notation"

- freckles

You can please define that for me.

- anonymous

ill take a picture of it

##### 1 Attachment

- imqwerty

i think you are talking about multiplicative inverse? u in 6or7th grade?

- anonymous

Alright this is it

##### 1 Attachment

- anonymous

No Ive just been out of school for five years

- freckles

\[\frac{1}{a}=a^{-1}\]
@imqwerty made a great guess earlier

- 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

yea :D

- anonymous

So where is a good place to practice this because I really don't have a clue how you go the answer.

- freckles

you see the exponent 3

- freckles

on the bottom there?

- anonymous

yup

- freckles

\[\frac{1}{5x^3}=\frac{1}{5} \frac{1}{x^3}=\frac{1}{5} x^{-3} \text{ use the rule I gave }\]

- freckles

bring that little part to the numerator and change the sign of the exponent

- anonymous

That makes sense now.

- 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

ah I see. This was easier than what I made it seem.

- Rushwr

\[\frac{ 1 }{ 5x ^{3} } = y\]
\[5y= \frac{ 1 }{ x ^{3} }\]

- Rushwr

\[\sqrt[3]{5y} = x\]

- 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

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

|dw:1441192519704:dw|

- anonymous

Thanks @Rushwr

- 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

is this an american class?

- anonymous

@freckles yeah i figured as much thats why I was looking for a site to practice on.

- anonymous

@freckles its an entrance exam

- freckles

most of the sites I can find go backwards
they want positive exponents instead of negative exponents

- 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

@freckles its cool I appreciate all of your help. I will most certainly check the website out at this point anything will help.

- 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

Thanks guys! I have to go. have a good day all!

- freckles

you too

- 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

@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

they should have said write with negative exponents

- freckles

and I based this on their solutions

- 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

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

but
\[\frac{1}{5}x^{-3} \text{ is \not the multiplicative inverse of } \frac{1}{5x^3}\]

- freckles

oh I think I get what you are saying so why wouldn't the answer be:
\[(5x^3)^{-1} \text{ instead }\]

- 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

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

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

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

are weird*

- mathmate

Yes, I agree that "write with negative exponents" would be more suited for the "correct " answer.

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