Reciprocal of fraction with negative exponent, Please explain what is wrong with my answer

[Volume1337]

My question word to word "Evaluate the Reciprocal of the following situation and show all steps. (Do not leave answer as a fraction)".

(-5/0)^-3

my answer = 0
actual answer = undefined

this may be simple but it's so confusing for me.
I'm attaching my process and solution by teacher as well.
I want someone to explain what exactly did I do wrong, I have a test in few hours and teacher is not available right now to explain.

link to work -> https://ibb.co/C5wMv4b

 

[R.M.]

I think you got hung up on the wording of the problem. "Evaluate the reciprocal". A reciprocal is the same a power of -1.
[(-5/0)^-3]^-1 --> (-5/0)^3 --> undefined

 

[Volume1337]

I think you got hung up on the wording of the problem. "Evaluate the reciprocal". A reciprocal is the same a power of -1.
[(-5/0)^-3]^-1 --> (-5/0)^3 --> undefined

oh so it was a trick question kind of

 

[Dr.Peterson]

My question word to word "Evaluate the Reciprocal of the following situation and show all steps. (Do not leave answer as a fraction)".

(-5/0)^-3

my answer = 0
actual answer = undefined

this may be simple but it's so confusing for me.
I'm attaching my process and solution by teacher as well.
I want someone to explain what exactly did I do wrong, I have a test in few hours and teacher is not available right now to explain.

link to work -> https://ibb.co/C5wMv4b

You effectively took the reciprocal twice, by both flipping the inside and changing the sign of the exponent.

What R.M. did is what I would have done; your teacher took the reciprocal of the inside and then simplified.

 

[HallsofIvy]

5/0 does not exist (is "undefined"). Any formula involving it gives a number that does not exist (is "undefined"0.

 

[Steven G]

You can not take the reciprocal of an undefined number. For the record (-5/0) is undefined making (-5/0)^-3 undefined and finally making the reciprocal of an undefined number undefined.

Out of curiosity what do does arrow mean??

 

[Volume1337]

You can not take the reciprocal of an undefined number. For the record (-5/0) is undefined making (-5/0)^-3 undefined and finally making the reciprocal of an undefined number undefined.

Out of curiosity what do does arrow mean??

the arrow between the first two, that's something I just do out of habit, teacher said you must never ever write = when taking reciprocal and I just have a bad habit of writing = when expanding or solving equations. so I do small arrow just to make myself not write = accidently

 

[Steven G]

the arrow between the first two, that's something I just do out of habit, teacher said you must never ever write = when taking reciprocal and I just have a bad habit of writing = when expanding or solving equations. so I do small arrow just to make myself not write = accidently

The message you got from your teacher is wrong (the teacher said it correctly!)

For example, The reciprocal of 2/3 is 3/2. So you should not write 2/3=3/2. However, since the reciprocal of 2/3 can be written as (2/3)^-1 you most definitely can write (2/3)^-1=3/2.

Now, if it wasn't for the fact that -5/0 is undefined you can write [(-5/0)^-3]^-1 = (-5/0)^3