exponential squared

Question

I have the following equation

$$v=ac\exp(-ct)$$

If I square this equation, is the following correct?

$$v^2 = a^2c^2\exp(-ct)*\exp(-ct) = a^2c^2\exp(-2ct)$$

This result is because:

$$e^{(x+y)} = e^xe^y$$

"e" and "exp" are the same thing.