2. Monomial is an expression that is a
number, a variable, or a product of a
number and variables.
Constant is a monomial containing no
variables.
Coefficient is a numerical factor of a
monomial.
Degree is the sum of the exponents of a
monomial’s variables.
Power is the expression of the form xn.
3. Laws of Exponents
1
Negative Exponents: a −n
= n
a
1
a
−n =a n
m +n
Multiplying Powers: a g a = a
m
n
4. Laws of Exponents
m
a m −n
Dividing Powers: n =a
a
Power of a Power: (a ) =a
m n mn
( ab )
m
Power of a Product: =a b m m
5. Laws of Exponents
n n
a a
Power of a Quotient: = n
b b
−n n
b a
= bn
a
Power of Zero: a = 1
0
6. Examples using the laws of exponents:
1. (2ab )(−3a b c ) = −6a b c
2 4 2 5 4
2. (6x y2 3
)(−xyz ) = −6x y z
3 4
12
x
3. 4 = x 8
x
7. −10x y 2 4
4. 4 = −2x
5xy
5. (x )= x
2 4
8
6. (−2a b ) = 16a
3 2 4
12 8
b
8. 2
3x y
3 n
7. 5 3n 2
x y z
2
3 9
= 2 2n 2 = 4 4n 4
x y z x y z
9. −3 3 3
4 n n
8. = =
4 64
n
−3 −3
3x y x
3b 2b
9. b 3 = 2
−6x y −2y
2 3
−2y −8y 6
= 2b = 6b
x x