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May 24th

May 24th

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

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:

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