# Polynomials

# 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 2^{x}. 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.

### Sample Problem

What is (3^{x})(3^{4x})?

Since the base is the same, we add the exponents to get 3^{5x}. 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.