If (e^x)^-2 X (e^x)^2 X e^x = 1/e^2
find x?
I have no idea how to do this.
I suggest a * to stand for multiplication, so we do not have to guess if X is a variable or an operator.
(e^x)^(-2) * (e^x)^2 * e^x = 1/e^2
The left hand side simplifies easily using the law of exponents:
(e^x)^(-2+2) * e^x = 1/e^2
1 * e^x = 1/e^2
e^x = e^(-2)
x=-2