Adding exponents in algebra?

Question

When simplifying an equation such as $x^4 + x^4$, I know the answer is $2x^4$, but what I don't understand is why don't you add the exponents along with the $x$? $x^4$ is $x \cdot x \cdot x \cdot x$, right? So why can't you simplify/add them, and have the answer be $2x^8$?

Answer 1

For example, $2^{4} + 2^{4}$ would not equal $2(2)^{8}$.