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UNIT 4 : EXPONENTIAL
& LOGARITHMIC FUNCTIONS
LESSON 1:
LAWS OF EXPONENTS
Examples of Powers:
25
= 2 x 2 x 2 x 2 x 2 = 32; (-3)3
= (-3) x (-3) x (-3) = -27; 2.72
= 2.7 x 2.7 = 7.29
A POWER (am
) consists of two parts; the base “a” and the exponent “m”.
Review of Basic Exponent Laws:
|
Rule |
Example |
Explanation |
|
am x an = am+n |
32 x 35 = 37 |
Multiplication Rule - If the bases are the same, add the exponents |
|
|
|
Division Rule - If the bases are the same, subtract the exponents |
|
(am)n
= amn |
(32)3=36 |
Power Rule – When taking a power of a power, multiply the exponents |
|
(ab)m
= amam |
(3 x 2)4 = 34
x 24 |
Power of a Product – Take each factor in the product to that power |
|
|
|
Power of a Quotient – Take numerator and denominator to that power |
Example 1: Simplify.
Solutions:
Example 2: Simplify.
Solutions:
Example 3: Simplify each of the following:
Solutions:
Alternate solution for c):
Rational
Exponents:
Review
of Radicals and Roots:
Example 2:
Example 4: Simplify
Solutions:
Example 5: Simplify
Solutions:
Example 6: Simplify
Solutions:
