Re: [Mathematica] simplification question of (1/x)^n * x^n ----> 1 ?

"Nasser Abbasi" <nma@xxxxxxxxx> wrote:
"Bhuvanesh" <BhuvaneshBhatt@xxxxxxxxx> wrote in message
news:6285672.1191198802693.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxxxxx
(1/x)^n*x^n is not always 1.

In[1]:= (1/x)^n*x^n /. {x->-1, n->Pi}

2 Pi
Out[1]= (-1)

In[2]:= N[%]

Out[2]= 0.629682 + 0.776853 I

Bhuvanesh,
Wolfram Research

Thanks. It seems the thing that makes the difference is if one cay carry
the exponent inside the brackets or not.

When doing this by hand, when I see (a/b)^n, I can rewrite it as (a^n
/ b^n) right? at least I hope so :)

No. For example (essentially the same example I mentioned at the end of my
previous response), suppose a = 1, b = -1 and n = 1/2. Then

(a/b)^n = (1/(-1))^(1/2) = (-1)^(1/2) = i

while

a^n/b^n = 1^(1/2)/(-1)^(1/2) = 1/i = -i instead.

David

I think this is called the dividing
of powers rule of something like that. (high school stuff.)

So the question now is this: is (1/x)^Pi = 1/x^Pi ? According to
Mathematica these are NOT the same.

Yet when type 1^Pi Mathematica responds with 1.
And when I type (1/x^Pi)*x^Pi it also gives 1.
And when I type (1^Pi/x^Pi)*x^Pi it also gives 1.

So, This must mean that (1/x)^Pi is not the same 1/x^Pi becuase that
is the only thing that is stoping it to be 1.

And this is the part that I do not understand.

Nasser
.

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