Exponential notation is useful for repeated factors, such
as:
a · a · a · b · b · c · c · c · c = a3b2c4
Terminology: an = a · a · a · · · ·a, where a is a factor
n times .
Be aware of the difference between :
a. −32 which represents −9 and
b. (−3)2 which is equivalent to 9
The fol lowing definitions are used to simplify algebraic
expressions :
When simplifying expressions, use the following laws of
exponents:
Properties of nth roots
Scientific Notation: (used on extremely large or
extremely small numbers)
• to rewrite any number as a number between 1 and 10 multiplied times a power of
10
• a × 10n where 1 ≤ a < 10 and n is an integer
• 34,000,000 = 3.40 x 107
• 2,570 = 2.57 x 103
• .00000028 = 2.8 x 10-7
Ex press the following in scientific notation:
1. 30,194
2. .0100028
Rational Exponents :
EXAMPLES:
Definition:
is changed into a = bn by raising both sides of the equation to the
nth power. note: if n is even, then a ≥ 0 and b ≥ 0
Combining Radicals
Simplify:
Find the like terms :
Sometime n one appear to be like terms, ie:
Rationalizing the Denominator: In mathematics , it
is preferred that no radical ap -
pears in the denominator. We eliminate radicals by multiplying by the conjugate
when there
are two terms in the denominator.
EXAMPLES:
Rational Exponents:
EXAMPLES:
Special cases to watch out for!
•
which can be written as
Does that mean
?
• however
is NOT −3
• definition:
• In general, if you take an even root and the solution has an odd exponent,
absolute
value signs are required .
• ie:
or more simply k2n4· | mp3 |
Example:
