Download Unit 2 Day A Worksheet

Unit 2 – Exponents & Polynomials
Algebra 2A
Unit 2 Day A ~ Rules of Exponents
WHRHS
2011-2012
Rules & Definitions of Exponents:
A. Multiplication - x m  x n  x m n
xm
B. Division - n  x m  n
x
 
C. Exponents Raised to Exponents - x m
n
 x m n

D. Exponential Expressions Raised to Exponents - x m y n
E. 0 as an Exponent -

p
 x m p y n  p
x0  1
00 undefined
1
xm  m
x
F. Negative Exponents 1
 xm
m
x
*Remember negative exponents DO NOT mean negative numbers.
*Watch where the parentheses are when you are working with exponents. Everything inside the
parentheses is raised to the exponent.

Monomial - a Number, a Variable or a PRODUCT of a number and a variable.
*monomials cannot have radicals with variables inside, quotients of variables or
variables with negative exponents.

Degree of a monomial - is the SUM of the exponents of the variable(s) in the monomial. The
degree of a constant term is 0.
RULE 1: Multiplying Exponential Expressions: PRODUCT OF POWERS RULE
If m and n are positive integers, x m  x n  x m  n
Example: Simplify (5a 2b4 )(2ab5 )
Example: Simplify (7 xy3 )(5x2 y 2 )( xy 2 )
WHRHS
Unit 2 – Exponents & Polynomials
2011-2012
Algebra 2A
RULE 2: Simplifying a Power of an Exponential Expression: POWER OF A POWER RULE
If m and n are positive integers, ( x m )n  x mn
RULE 3: Simplifying Powers of Products: POWER OF A POWER RULE
If m,n, and p are positive integers, ( x m y n ) p  xmp y np
Examples:
Simplify the following
A) ( x 4 )5
B) ( x 2 ) n
C) (2a3b4 )3
D) (2ab)(3a)2  5a(2a 2b)
RULE 4: Definition of Zero as an Exponent
If x does not equal zero, then x 0  1 .
RULE 5: Definition of a Negative Exponent
If x does not equal and n is a positive integer, then x  n 
1
xn
RULE 6: Dividing Exponential Expressions: QUOTIENT OF POWER RULE
xm
If m and n are positive integers, n  x m  n
x
7
x
Example: Simplify 3
x
RULE 7: Simplifying Powers of Quotients: QUOTIENT OF POWER RULE
p
 xm 
xm p
If m,n, and p are integers and y does not equal zero, then  n   n p
y
y 
 a2 
Example: Simplify  3 
b 
2
EXAMPLES:
Simplify:
2
3
4
5
A) (3x y )(6 x y )
C)
x 2 y 4
x 5 y 2
 3a 2b 2 c 1 
B) 
1 2 4 
 27a b c 
2
Unit 2 – Exponents & Polynomials
Algebra 2A
WHRHS
2011-2012
Unit 2 Day A Worksheet:
1.
(3)
 2
2.   
 5
3
 3
3.    
 7
2
3
5.    m  


7.
 
 x3 2 


13.

6.
 a b c 
3
5
2 4

 11a 5 
10.   3 
 6c 
r 3 p  rp 
r p 
2
b
15.  2a 


3
8.     p3 

 
 c 

6
p5 w
 pw2 p 3 w3
4
4.
6
w2 x 4
9.
 w2 x 5
11.
3
2
a b 
 a b 
2 5

12.
2
5
5
2
2
5
 
14. 5 5 x
c
16.
m  m 
2 k 1
2
k 2
3
Unit 2 – Exponents & Polynomials
Algebra 2A
WHRHS
2011-2012
18.
 y 2n 
19.  n  2 
y 
21.
3 
x y
k x2
17. 2  x
k
3
22.
24. a 2
 3u 
27.
 20kn   4k
29.
 3a  b c
 6   a b 
3
3
3
1
5 1
10
2
25.
3
32 x  y
20. 12  43 
2 2
8
  3 3 
23.  2 
 3 
2
26.
1
2
1 2
n
2 4
2 3
2
c 6

2
 3r   r 
2
 2 n 
3
28.
2
3
2
4 n 5
 22 r 2 s 1 
30. 
3 
 2rs 
2