- 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

If you're still not sure what exponents are, feel free to travel back in time to Unit 1. We're traveling to whatever planet polynomials are from in this little fantasy of ours, so we don't see why you shouldn't be able to time travel as well. Bring back some baseball stats for us!

In addition to the whole number exponents we talked about earlier, exponents can also be negative, rational, and even irrational.

While they can get freaky, exponents still play by some rules.

**Rule #1: The Additive Exponent Rule.** Multiplying two powers of a number is the same as adding the exponents.

In symbols, this says that (*x*^{a})(*x*^{b}) = *x*^{a+b}. Here's a real number example:

(7^{5})(7^{3}) = 7^{5+3} = 7^{8}

**Rule #2: The Multiplicative Exponent Rule.** If you are taking the power of an exponent (the exponent of an exponent), then you multiply them. Hopefully you will never need to take the exponent of an exponent of an exponent, because that exponent would be extremely tiny, and you would need a stronger prescription contact lens to read it. We'll keep our eyes crossed for you.

In symbols, this is *x*^{(a)b} = *x*^{ab}. Or, in real numbers, 14^{(2)50 }= 14^{100}

Exercise 1

Is 2^{3} × 2 equal to 2^{2} × 2^{2} × 2^{2}?

Exercise 2

What is (4^{3} × 4^{5})^{2}?

Exercise 3

Does (*a ^{b}*)