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

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

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

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

5. 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

6. Simplify (p2)4 p2 p4 p8
p16

7. 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

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

9. 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

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