Question

If (e^x)^-2 X (e^x)^2 X e^x = 1/e^2

find x?

I have no idea how to do this.

Answer 1

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