Why does exp(x+y) NOT equal exp(x)+exp(y)? [A-level Maths and Further Maths common mistake]

This is a very common mistake, so don't worry. To see why this is the case, let's go back through our notes to the "laws of indices" and recall the rule for adding powers; a^m * aⁿ = a^(m+n) The exponential function e^x (we can also write it as exp(x)) also follows these laws of indices, so; e^x * e^y  = e^(x+y).......... NOT e^x + e^y