Question

just to make sure... (e^(-2t))^2 = e^(4t) right?

Answer 1

no, it is e^(-4t)

Answer 2

-2^2 = -4
so agdgdgdgwngo is correct.

Answer 3

er yeah negative

Answer 4

-2^2 = -4 (-2)^2 = 4 order of operations ;)

Answer 5

oh right :-P

Answer 6

hmm wait a minute, I thought unary minus has precedence over the binary exponentiation

Answer 7

so -2^2 = (-2)^2 = 4

Answer 8

but my calculator says exponentiation has higher precedence... so :-(

Answer 9

http://www.wolframalpha.com/input/?i=-2%5E2

Answer 10

I believe, exponentiation has almost the highest order. Also, the parenthetical statement can be said as such:
-2^2 = -1(2^2) = -1(4) = -4
Whereas:
(-2)^2 = (-2)*(-2) = 4

Answer 11

For the record,
\[(a^x)^y = a^{xy} \ \ \text{ NOT } \ \ a^{x^y}\]

Answer 12

Hence
\[(e^{-2x})^2 = e^{-4x}\]