- Topics At a Glance
**Exponents**- Negative Exponents
- Fractional Exponents
- Irrational Exponents
**Variables as Exponents**- Defining Polynomials
- Degrees of a Polynomial
- Multivariable Polynomials
- Degrees of Multivariable Polynomials
- Special Kinds of Polynomials
- Evaluating Polynomials
- Roots of a Polynomial
- Combining Polynomials
- Multiplying Polynomials
- Multiplication of a Monomial and a Polynomial
- Multiplication of Two Binomials
- Special Cases of Binomial Multiplication
- General Multiplication of Polynomials
- We'll Divide Polynomials Later!
- Factoring Polynomials
- The Greatest Common Factor
- Recognizing Products
- Trial and Error
- Factoring by Grouping
- Summary
- Introduction to Polynomial Equations
- Solving Polynomial Equations
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

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.

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.

Example 1

Evaluate 4 |

Exercise 1

Find .

Exercise 2

Evaluate 25^{x} for .

Exercise 3

Find (5^{x})^{2}.