1. Objectives You will be able to:
1. Multiply monomials.
Simplify expressions with monomials.
Divide Monomials
Simplify negative exponents.

2. A monomial is a 1. number, 2. variable, or
3. a product of one or more numbers and variables.
Examples: 5 y
3x2y3

3. Why are the following not monomials? x + y
addition
division
2 - 3a
subtraction

4. Multiplying Monomials
When multiplying monomials, you ADD the exponents.
1) x2 • x4
x2+4 x6
2) 2a2y3 • 3a3y4
6a5y7

5. Simplify m3(m4)(m) m7 m8
m12
m13

6. Power of a Power
When you have an exponent with an exponent, you multiply those exponents.
1) (x2)3
x2• 3 x6
2) (y3)4
y12

7. Simplify (p2)4 p2 p4 p8
p16

8. Power of a Product
When you have a power outside of the parentheses, everything in the parentheses is raised to that power.
1) (2a)3
23a3
8a3
2) (3x)2
9x2

9. Simplify (4r)3
12r3
12r4
64r3
64r4

10. This is a combination of all of the other rules.
Power of a Monomial
This is a combination of all of the other rules.
1) (x3y2)4
x3• 4 y2• 4
x12 y8
2) (4x4y3)3
64x12y9

11. Simplify (3a2b3)4
12a8b12
81a6b7
81a16b81
81a8b12

12. When dividing monomials, subtract the exponents.1. 2.
= b5-2
= b3
= m7-1n5-2
= m6 n3

13. = xy
= 9a3b2

14. Simplify
48g2h2
48gh2
4g2h2
4gh2

15. = 1m0n = n Here’s a tricky one! They canceled out!
What happened to the m?
They canceled out!
There are no m’s left over!
This leads us to our next rule…

16. Zero Exponents Anything to the 0 power is equal to 1. a0 = 1
True or False? Anything divided by itself equals one.
True!
See for yourself!

17. Negative Exponents
A negative exponent means you move the base to the other side of the fraction and make the exponent positive.
Notice that the base with the negative exponent moved and became positive!

18. Simplify.
x-4 y0 You can not have negative or zero exponents in your answer.

19. Simplify p2
p12 .

20. Simplify.
You can’t leave the negative exponent!
There is another way of doing this without negative exponents.
If you don’t want to see it, skip the next slide!!!

21. Simplify (alternate version).
Look and see (visualize) where you have the larger exponent and leave the variable in that location. Subtract the smaller exponent from the larger one.
In this problem, r is larger in the numerator and s is larger in the denominator.
Notice that you did not have to work with negative exponents! This method is quicker!

22. Simplify.
Get rid of the negative exponent.

23. Simplify.
Get rid of the negative exponents.

24. Get rid of the negative exponents.
Simplify.
Get rid of the parentheses.
Get rid of the negative exponents.

25. Simplify .

26. Homework
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