prove that exp(x+y) = exp(x).exp(y)

Question

anonymous · Answer

Are you supposed to use this as the definition of exp(z)?$$\exp (z)=\lim_{n \rightarrow \infty} \left (1+\frac{z}{n}\right )^n~,~n \in \mathbb{N} $$Because there are alternate definitions that lead to the same consequences...

anonymous · Answer

$$\large x^{a+b} = x^a \times x^b$$

anonymous · Answer

What are the restrictions on x and y? Real? Complex? Rational? Integer? Whole number????

anonymous · Answer

Matrix?

anonymous · Answer

its real

anonymous · Answer

just prove me with that definition.. pls..

anonymous · Answer

exp or e is just a value and can be substituted for x in the equation waterineyes provided
e=2.71828...

anonymous · Answer

@sudhayesian remember when bases are same then we add up the powers like this:

$$\large x^a \cdot x^b = x^{a+b}$$

So opposite of this is : when exponents are in addition form in the same base then we can separate them in multiplication of bases form:
$$\large x^{a+b} = x^a \cdot x^b$$