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.
- multiplication property
- negative exponents
- division property
- power property