- 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

Let's kick things up a notch. It's time to introduce irrational exponents. You'll never need another Red Bull again if you can get addicted to these bad boys. What does 2^{π} mean, for example? We can't possibly multiply π copies of 2 together, can we? Even if we could, wouldn't that get awfully messy?

While we can't write out all the digits of π, we can **approximate** π using decimals:

π ≈ 3 (not a great approximation)

π ≈ 3.1

π ≈ 3.14

π ≈ 3.141 and so on.

We can use these approximations of π to approximate 2^{π}.

2^{π} ≈ 2^{3}

2^{π} ≈ 2^{3.1}

2^{π} ≈ 2^{3.14}

2^{π} ≈ 2^{3.141}

Since our approximations of π are rational numbers, we can find 2^{3}, 2^{3.1}, and so on. We'll never be able to write down all the digits of 2^{π}, in the same way that we'll never be able to write down all the digits of π. Don't beat yourself up about it. Do what mathematicians do. Throw your hands in the air, give up on the thought of arriving at an exact answer, and PART-AY!

Uh, estimate. That last one was supposed to be "estimate."