Variables as Exponents
Since exponents can be any real number and variables are basically the alien decoys of real numbers, we can write down expressions like 2x. We don't love to do it, but we can. We can evaluate these expressions for given values of x, multiply them together, and do whatever else we want to do with them as long as our mother approves. Parents first, algebra second.
What is (3x)(34x)?
Since the base is the same, we add the exponents to get 35x. Two players with the same base...that would never fly in baseball. Fortunately, in algebra, they can pile onto the same base as much as they like.