Laws of Exponents
Recall:
Positive integer exponent
Zero exponent
Negative integer exponent
Note: a -n is the reciprocal of a n
The exponent laws apply to numerical and variable bases. When the base is a
variable, we assume that it is not 0.
Multiplication Law:
Division Law:
Power of a power law:
(m and n are any integer)
A simplified algebraic expression contains onlypositive exponents.
Example 2: Evaluate each expression for a=1, b=­2, and c=3.
a)
b)
Example 1: Simplify. Evaluate where possible.
a)
b2 x b4 =
d)
b2 ÷b3 =
b)
c)
b-8 x b5 =
(b2 )3 =
c)
e)
(b4 )-1 =
f)
g)
h)
Example 3 (Pg. 363: #8):Computer power has been doubling approximately every 2
years as more and smaller transistors have been integrated to build better
computer chips. The number of transistors, T, in a chip has increased according to
T = 4500(1.4)n, where n is the number of years since 1974. Determine the number
of transistors in a computer chip in each year.
a) 1974
b) 2015
Homework: Pg. 362 #1 ­ 6, 10, 11cd, 12, 13, 15
1