# RWM102 Study Guide

## Unit 7: Operations with Monomials

### 7a. Apply the rules of exponents to simplify algebraic exponential expressions

- What happens when you multiply two monomials?
- What does a negative exponent mean, and how can you change a negative exponent to a positive exponent?

**Exponents **are simply a shorter way to write repeated multiplication. Since , when we try to simplify , we need to remember this is four 2's multiplied with three 2's, meaning we have seven 2's multiplied together, or . We can therefore see that **multiplication property** states: . Similarly, .

When dealing with exponents, you may come across a **negative exponent**. A negative exponent doesn't mean the answer will be negative. Instead, it means to take the **reciprocal **of the value, what you might call "flipping it". For example, simply means the reciprocal of , which is . Similarly, if there is a negative exponent in the **denominator **of a fraction, it moves the term to the **numerator**. For example, .

To review, see:

### 7b. Multiply, divide, and simplify the powers of monomials

- How do you divide monomials with exponents?
- How do you take an exponent to another exponent?
- How do you multiply and divide different monomials?

When we divide **monomials **with exponents, we subtract our exponents, rather than adding, like we do when we multiply. For example, . Therefore, the **division property** states: . Similarly, .

Sometimes, you might even have an exponent taken to another exponent, such as . When this happens, you need to multiply the exponents, giving us . Therefore, the** power property** states: . Similarly, .

We don't have to just multiply and divide the same monomial, we can multiply different monomials as well. To simplify the expression , we will multiply the numbers as normal, and then add the exponents on the variable, giving us .

Finally, we can divide different monomials. For example, can be simplified by first simplifying the numbers in the fraction, then using the division property to subtract the exponents, giving us an answer of .

To review, see:

- Exponential Properties Involving Products
- Exponential Properties Involving Quotients
- Multiplication Properties of Exponents
- Dividing Monomials

### Unit 7 Vocabulary

This vocabulary list includes terms listed above that students need to know to successfully complete the final exam for the course.

- exponents
- multiplication property
- negative exponents
- reciprocal
- denominator
- numerator
- monomials
- division property
- power property