Exponent Laws
Summary of the exponent laws:
Other rules and notes
 REMEMBER THAT ONLY PARTS/CHUNKS THAT ARE MULTIPLIED OR
DIVIDED CAN BE CANCELLED.
 Things that are in brackets are considered chunks. If
there is an identical chuck then the two can be
manipulated (cancelled).
Â· If there are addition or subtraction between terms, then
one will need to remove those by FACTORING. Remember terms that
are added or subtracted are not covered by the exponent laws.
Â· If we can find a number so that the bases are the same,
then the exponents must also be the same
Â· If the value of two numbers is the same, and we know one
base, we know the 2 nd by default, because they must be the same
Â· Use a trial and error approach to solve for unknown
exponents and/or bases
Simplifying Powers
(3a^{ 2} b)(2a^{ 3} b^{ 2}) = 3 Ã—
(2) Ã— a^{ 2} Ã— a^{ 3} Ã— b Ã— b^{ 2} =
6 a ^{2 + 3 }b^{ 1 + 2} = 6a^{ 5} b^{
3}
Only variables which are the same can be used together. When
two variables are being multiplied we ADD their exponents.
Power of a quotient
Â· Reduce the quotient before you bring in the exponent.
o Same as adding exponents, but if they are in the denominator
they are subtracted.
o
Â· When an exponent is to an exponent, we multiply the numbers
together
Negative Exponents
Â· We can clear negative exponents by taking the reciprocal
o If it is a quotient, you can subtract the negative (hence
making it positive)
Special Cases
An exponent of Zero = 1, 0^{ 0} is not defined, there
is an understood exponent of 1 if no other number appears.
