Hard Math Question

[#M|A#Wolf]

Whoever simplifies this equation correctly gets my unconditional love for a week and chocolates through PayPal. And no, it's not my homework you skeptics.

[Mael]

(a^m)^m*(a^-m)^m-n

[Oracle]

((a^(m+n))/(a^n))^m = ((a^m)(a^n)/(a^n))^m = (a^m)^m = a^(m^2)
(a^(n-m))/(a^n))^(m-n) = ((a^n)(a^-m)/(a^n))^(m-n) = (a^-m)^(m-n) = a^(-m^2+mn)

Product of those two = a^(m^2-m^2+mn) = a^(mn)

[RCJD]

a^(3mn-n^2-2n)

edit: nice ShadZ!

[Cho]

Just guessing here:

((a^m)^m)((1/a^m)^m-n)

EDIT: heres a pic: http://www.mathway.com/math_image.aspx?p...p=109?p=42

[Oracle]

Mfw people are getting different answers from me ('cept Mael, his is just unsimplified)

Your feeble skills are no match for the power of the Dark Side! You have paid the price for your lack of simplification!

[Habluka]

Whoever simplifies this equation correctly gets my unconditional love for a week and chocolates through PayPal. And no, it's not my homework you skeptics.

It looks perfectly fine to me. Why simplify it?

[Mael]

I just copied the first answer on Wolfram.

[Sveark]

[Alien]

there will be some rules which i don't remember ofc :D but the input conditions are important


> f := (a^(m+n)/a^n)^m*(a^(n-m)/a^n)^(m-n);
print(`output redirected...`); # input placeholder
m (m - n)
/ (m + n)\ / (n - m)\
|a | |a |
|--------| |--------|
| n | | n |
\ a / \ a /

Shadow's output
> g := `assuming`([simplify(f)], [a > 0, m > 0, n > 0]);
print(`output redirected...`); # input placeholder
(m n)
a

Mael' output
> h := `assuming`([simplify(f)], [a::real, m::real, n::real]);
print(`output redirected...`); # input placeholder
m (m - n)
/ m\ / (-m)\
\a / \a /

[GDM]

shadz is correct.

Also: Alien, why is your post. You seem to be just regurgitating, in obfuscated syntax, what others have done.

---

Whoever simplifies this equation. . .

It looks perfectly fine to me. Why simplify it?

Because, if you are working out a computation with this element in it, a^mn is probably easier to work with.

[Marti]

> f := (a^(m+n)/a^n)^m*(a^(n-m)/a^n)^(m-n);
print(`output redirected...`); # input placeholder
m (m - n)
/ (m + n)\ / (n - m)\
|a | |a |
|--------|
| n | | n |
\ a / \ a /

looks like a gun lol ( with a bit of imagination)

[Alien]

i was lazy to upload image :) both solutions are correct, it depends on conditions :P for a^mn

> solve(m^2-m*(m-n));
print(`output redirected...`); # input placeholder
{m = 0, n = n}, {m = m, n = 0}

[Habluka]

---

Whoever simplifies this equation. . .

It looks perfectly fine to me. Why simplify it?

Because, if you are working out a computation with this element in it, a^mn is probably easier to work with.

I don't know, I always find it easier to make it look nicer by defining new variables. Of course this is coming from getting angry in high school classes where the the teachers were complete fascists about having answers simplified, which will only lead to more problems if you do it by hand.

[al3rt]

> f := (a^(m+n)/a^n)^m*(a^(n-m)/a^n)^(m-n);
print(`output redirected...`); # input placeholder
m (m - n)
/ (m + n)\ / (n - m)\
|a | |a |
|--------|
| n | | n |
\ a / \ a /

looks like a gun lol ( with a bit of imagination)

Looks like an 'F' to me