# EXPONENTS AND MONOMIALS by starli84

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```									Exponents and Monomials

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.

Negative Exponents:

Laws of Exponents

a

n

1  n a

1 a
m
n

a
n

n

Multiplying Powers: a  a  a 

mn

Dividing Powers: Power of a Power: Power of a Product:

Laws of Exponents

a n a

m

a
n

mn

a

m

 a
m

mn

 ab   a b

m m

Laws of Exponents
a a Power of a Quotient:    n b b  n n a b    bn a 0 Power of Zero: a  1
n
n

Examples using the laws of exponents:

1. 2ab

2

3a b c   6a b c
4 2

5 4

2. 6x y
12

2 3

xyz  6x y z
3 4

x 8 3. 4  x x

10x y  2x 4. 4 5xy
2 4

5.  x

4 2

 x
3

8

6.  2a b

4 2

  16a

12 8

b

 3x y  7.  5 3n 2  x y z 
3 n

2

 3  9   2 2n 2   4 4n 4 x y z  x y z

2

 4 n  n 8.     4  64 n
 3x y   x  9.  b 3    2  6x y  2y  6 2 3 2y  8y   2b   6b  x  x
3b 2b 3 3

3

3

3

```
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