In order to be successful with polynomials, we must have a great understanding of exponents. We continue by looking at the quotient rule for exponents. We will then look at integer exponents. These properties will allow us to work more quickly with exponents.
Test Objectives:•Demonstrate a general understanding of exponents
•Demonstrate the ability to use the quotient rule for exponents
•Demonstrate the ability to work with integer exponents
Integer Exponents & the Quotient Rule Test:
#1:
Instructions: Simplify each.
a) (2x^{5}y^{3})^{-4} • -2y^{2}
b) (2m^{3}n^{-4})^{-3} • -2m^{5}n^{0}
#2:
Instructions: Simplify each.
a) 2x^{2} • (2x^{3}y^{-1})^{-3}
b)
[ | (-2n^{-4})^{2} • (n^{-4})^{5} | ] | 4 |
-n^{3} |
#3:
Instructions: Simplify each.
a)
- | pqm^{2} • pq |
(2mp^{2}q^{2})^{2} |
#4:
Instructions: Simplify each.
a)
(2pn^{-1})^{-2} • -2pm^{2}n^{-2} |
m^{2}n^{2} |
#5:
Instructions: Simplify each.
a)
2np^{2} • mn^{0}p^{2}(-2pm^{-1}n^{2})^{-1} |
-2pm^{2}n^{-2} |
Written Solutions:
Solution:
a)
- | 1 |
8x^{20}y^{10} |
b)
- | n^{12} |
4m^{4} |
Solution:
a)
y^{3} |
4x^{7} |
b)
256 |
n^{124} |
Solution:
a)
- | 1 |
4p^{2}q^{2} |
Solution:
a)
- | 1 |
2pn^{2} |
Solution:
a)
p^{2}n |
2 |