- 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

Negative exponents are basically abbreviations for big ugly fractions. In the same way that it's quicker to write LMAO in place of the longer version, negative exponents will make it much easier to text all your friends about algebra. We know that's what 95% of all your texts are about. You're so obsessed.

Let's start with a simple example. What would *x*^{-1} mean? Well, we know that *x* = 1 as long as *x* isn't zero. Using this information, we can apply the additive rule to see that

*x*^{-1} × *x*^{1 }= *x*^{-1+1 }= *x *= 1

In other words, *x*^{-1} is the **multiplicative inverse** or **reciprocal** of *x*^{1}=*x*. Therefore, . Got that, Fraction Jackson?

*x*^{-2}is the reciprocal of*x*^{2}, that is, .

- 2
^{-3}means .

- .

Make sure you put negative exponents in that part of your brain where you keep things, right in between the cheat codes for *Street Fighter* and the fantasy stats for every professional baseball player. They will be important when you learn **scientific notation**, which we'll talk about later. You will need to hang in there and notate stuff unscientifically until then.

Example 1

Rewrite the expression |

Exercise 1

Rewrite the following expression without negative exponents, simplifying if possible:

*x*^{-4}

Exercise 2

Rewrite the following expression without negative exponents, simplifying if possible:

2^{-5}

Exercise 3

Rewrite the following expression without negative exponents, simplifying if possible:

(-2)^{-3}