The Product Rule of Exponents
For any real number
a and natural numbers
m and
n, the product rule of exponents states that
am⋅an=am+n
The Quotient Rule of Exponents
For any real number
a and natural numbers
m and
n, such that
m>n, the quotient rule of exponents states that
anam=am−n
The Power Rule of Exponents
For any real number
a and positive integers
m and
n, the power rule of exponents states that
(am)n=am⋅n
The Zero Exponent Rule of Exponents
For any nonzero real number
a, the zero exponent rule of exponents states that
The Negative Rule of Exponents
For any nonzero real number
a and natural number
n, the negative rule of exponents states that
a−n=an1 and an=a−n1
The Power of a Product Rule of Exponents
For any real numbers
a and
b and any integer
n, the power of a product rule of exponents states that
(ab)n=anbn
The Power of a Quotient Rule of Exponents
For any real numbers
a and
b and any integer
n, the power of a quotient rule of exponents states that
(ba)n=bnan