Exponents and Multiplying Polynomials
Exponent Rules:
a a  a
m
n
mn
a
m
1
 
a
m
am
 a m n
n
a
Negative Exponents indicate that you
need to take the reciprocal.
a0  1
The negative sign in the exponent can
become the fraction bar in the result.
a 
m n
 amn
Multiply.
(-3y)(y)
(3a2)(-2a3b4)
(-5a2b3)(-4ab2)
(b2)(3a3)2
(x3y5)4
-3y2
(-22)3
(-2·2)3
(-4)3
(-4)(-4)(-4)
-64
Multiply.
(3y2w)(7x)
(xy3)(-xy4)
(2a2b)3
(-a3b2)(ab4)2
(-5r6)2
(-2x)(2x4)3
When reducing fractions, divide both the numerator and the denominator by the same factor.
Do NOT divide by a term!!!!
For these fractions, the fraction is not totally reduced if the same variable is in both the
numerator and the denominator.
In general, I would suggest that you:
 clear outside exponents first
 then remove parentheses
 then re-locate variables with negative exponents
 and finally reduce the fraction so that a variable is only in the numerator or denominator
but not both.
x2
x
xx
x
x
y3
y5
14m11
 7m10
Simplify.
1
a 3
(2 w 3 z )( 3z 4 )
 12 wz
24a 2b7c9
36a 7b5c
n
n6
w-10
2x 1 y 4
x2 y3
Use any of the appropriate properties of exponents to simplify the expressions.
Your answers should contain only positive exponents.
x2 y
x 4 y 3
 6ab 4 


2
 3b 
3
x 2 yy 3
x4
 3b 2 

4 
 6ab 
x2 y4
x4
b6
8a 3b 12
y4
x2
b18
8a 3
x 
 1 
 2
x 
1
x6
3
2 3
3
Use any of the appropriate properties of exponents to simplify the expressions.
Your answers should contain only positive exponents.
3x 
 4u
12m4
4mn5
 a 2b  a 3b 
 2  3 
 ab  b 
 2 1
6 8
v
 6u
4 2
v

Use any of the appropriate properties of exponents to simplify the expressions.
Your answers should contain only positive exponents.
3 x  2x
x 
2 3
4 2
4
2 6
 6a b 
 8a 4b0 


2
Exponent Rules
More Exponent Rules :
1
1
a m  m
a m  a ma
and
n
m
a m  an
Negative Exponents indicates that you need to take the reciprocal of the base.
The negative sign in the exponent is rewritten as the fraction bar in the
resulting simplification.
The denominator of the exponent is the index of the radical!
Index
81/ 3
3
8
=2
Base
When working with rational exponents, if the denominator of the exponent
(which is the index of the radical) is even both the radicand and the
simplification must be positive. If the leading coefficient is negative, the
answer could be negative.
Simplify each expression. Use absolute Value symbols when necessary.
Write all your answers without using negative exponents.
1/ 3
64
 16 


 625 
1/ 4
1/ 2
 9 
 
 64 
Write an equivalent expression using radical notation, and, if possible, simplify.
100 ½
(9y6) 3/2
a 4/5
Write an equivalent expression using exponential notation.
33

6
5
2a b

7
5
x3 yz 2
Simplify each expression. Use absolute Value symbols when necessary.
Write all your answers without using negative exponents.

(125)2 / 3
625a 4b8

1/ 4
Simplify each expression. Write all your answers without using negative exponents.
Assume all variables are positive.
 32m10 
 
15 

 243n 
2 / 5
 27c d 


3
 f

2
3
1
3
Simplify each expression. Write all your answers without using negative exponents.
Assume all variables are positive.
2
73


3
79
27 2 / 3

3/ 2
6 3/ 8
6 1 / 8

55 / 4

3/ 8
Simplify.
12
b4
3 3
x
8
 3x 
2
15
 7z 
5