1. Lesson 7-1 Multiplying Monomials

2. What is a monomial?
A Monomial is a number, a variable, or a product of numbers and variables.
Monomials are similar to terms
Terms that are divided by a variable are not monomials.
Constants – monomials without variables (only numbers)

3. Examples Determine whether each expression is a monomial. -5 x Yes
No, contains addition
No, contains division of variables
Yes, could be written as

4. Review Powers Remember that means Similarly means So And
Can you think of a general rule?

5. Product of Powers
To multiply two powers that have the same base, add the exponents
For any number a and all integers m and n,
Ex. Simplify
Multiply all numbers
Combine all like
variables by adding exponents
Rewrite your answer

6. Problems to Try
Determine whether each expression is a monomial. Explain.
Simplify

7. More to think about
Consider
And
Can you think of a general rule?

8. Power of a Power To find the power of a power, multiply the exponents
For any number a and all integers m and n,
Ex. Simplify

9. One more…
Consider
And
Can you think of a general rule?

10. Power of a Product
To find the power of a product, find the power of each factor and multiply.
For all numbers a and b and any integer m,
Ex. Find the area of the square

11. Problems to Try Simplify 1.
2. Find the volume of a cube with side length

12. Simplifying Monomial Expressions
When a monomial is simplified:
There is only one of each variable
There are no powers of powers
All fractions are simplified
Ex. Simplify
(use order of operations)

13. Problem to Try
1. Simplify