Addition with variable in exponent

Question

I know that $2^x$+$2^x$=$2^{x+1}$ but I can not explain why. Googling returns too much information about the situation involving variable in the base. Can someone explain? A link to a reference would be sufficient. Thanks

Answer 1

$2^x+2^x=2\cdot 2^x=2^{x+1}$.

Answer 2

I think the others hit the nail in the head, however, I would just like to add the following general statement.

$$x^a*x^b=x^{a+b}$$

In our case, we have the expression:

$$2^x+2^x$$ Which can be rewritten as the equivalent expression:$$2(2^x)$$

Notice that we can apply our general statement to this as follows: $$2^1*2^x$$

Hence, you just "add" the exponents together to get $2^{x+1}$.