Why does a^n/m = (a^1/m)^n give different results?

[disregardthat]

My teacher gave us some rules about numbers in the power of brackets.

Like 2^1/2

It was: a^1/n= n'root'a

(instead of a square root (2'root') or cube root (3'root') it was n'root'.)

Anyway, that equation is correct, at least with the brackets i tryed it with. But when we get numbers that isn't "1/n", but "n/m" he gives us this equation:

a^n/m = (a^1/m)^n = (m'root'a)^n

This equation I can't make correct. For example: I do 2^3/2 on my calc, and it gives me this: "4"

I put it in the equation:

2^3/2 = (2^1/2)^3

When I write this new setup on my calc it gives me this: "1"

I put it in the other equation and do it on my calc:

2^3/2 = (2'root'2)^3

It gives me this: "2.8284..."

There are four possibilities:
- I must be doing it wrong
- The equation is incorrect
- My calc is broke
- The laws of mathematics have changed

I am terribly sorry for my topic, I just found out that I forgot to put the bracket power into these: ( )
I just leave it standing so it won't be spam until one of the mods deletes it...

 

[matt grime]

You are misusing the calculator

The third option is the correct answer.

The errors seem to be that you

1. cubed 2 to get 8 then divided 8 by 2 to get 4
2. You actually multiplied 2 by 1/2, rather than raising it to the power 1/2m, to get 1, then cubed 1.

 

[disregardthat]

yeah, I forgot the ('s...

So I raised the number to the power of 1 and then divided it by 2...
2^1/2
It really should stay like this: 2^(1/2)

When I do this it gets correct on my calc, sorry again...

 

[HallsofIvy]

My teacher gave us some rules about numbers in the power of brackets.

Like 2^1/2

It was: a^1/n= n'root'a

(instead of a square root (2'root') or cube root (3'root') it was n'root'.)

Anyway, that equation is correct, at least with the brackets i tryed it with.

Brackets? Don't you mean just fractions?

But when we get numbers that isn't "1/n", but "n/m" he gives us this equation:

a^n/m = (a^1/m)^n = (m'root'a)^n

This equation I can't make correct. For example: I do 2^3/2 on my calc, and it gives me this: "4"

I put it in the equation:

2^3/2 = (2^1/2)^3

When I write this new setup on my calc it gives me this: "1"

Be careful about parentheses (Which really are a kind of "bracket". Was that what you meant?) If you enter 2^1/2 just as you have written, your calculator will interpret that as 2^1 = 2 and THEN divide by 2: (2^1)/2= 1 and, of course, the third power of that is 1. Use, instead, 2^(1/2)^3. That should give you 2.9294...

I put it in the other equation and do it on my calc:

2^3/2 = (2'root'2)^3

It gives me this: "2.8284..."

There are four possibilities:
- I must be doing it wrong
- The equation is incorrect
- My calc is broke
- The laws of mathematics have changed

I am terribly sorry for my topic, I just found out that I forgot to put the bracket power into these: ( )
I just leave it standing so it won't be spam until one of the mods deletes it...

You might have guessed it was the first of your four possiblities !
But anyway, it is easy to fix. (A lot easier to fix than the fourth one would have been!)

 

[disregardthat]

Sorry, wrong word there, Indeed i meant "fractions" and not "brackets", or parantheses was it, is there any other kind of brackets? I didn't know.

Hehe, the last one was a joke :)

 

[complexPHILOSOPHY]

Do you still need help specifically with any of the mathematics or was it simply a calculator issue?

 

[disregardthat]

I don't need help, thank you :)

 

[HallsofIvy]

Just remember- there is no such thing as too many parentheses!