In this exercise we have used the Zero Exponent Property and the Negative Exponent Property. However, later in the book we will learn about other properties of exponents. We list some of them below.
Product of Powers Property
The product of two powers with the same non-zero base a and integer exponents m and n can be written as a single power with base a and exponent m+n.
a^m * a^n = a^(m+n)
Quotient of Powers Property
The ratio of two powers with the same non-zero base a and integer exponents m and n can be written as a single power with base a and exponent m-n.
a^m/a^n=a^(m-n)
Power of a Power Property
A power with a non-zero base a an integer exponent m that is raised to another integer exponent n can be written as a power with base a and exponent m* n.
(a^m)^n = a^(m* n)
For the rule to be true for a=0, both exponents must be greater than zero.
Power of a Product Property
A power with an integer exponent m whose base is the product of two non-zero factors a and b can be written as the product of two powers with bases a and b and the same exponent m.
(ab)^m = a^m b^m
For this rule to be valid when either a or b is 0, m must be greater than zero.
Power of a Quotient Property
A power with an integer exponent m whose base is a ratio of a non-zero numerator a to a non-zero denominator b can be written as the ratio of two powers with bases a and b and the same exponent m.
(a/b)^m=a^m/b^m
For the rule to be true for a=0, m must be greater than zero.
