Question 896005
the formula when dealing with exponents is as follows:


(a*b)^x = a^x * b^x


(a/b)^x = a^x / b^x


assume a = 4 and b = 2


a^3 * b^3 is equal to (a*b)^3


you get:


4^3 * 2^3 = 64 * 8 = 512


by the formula, however, you get:


4^3 * 2^3 = (4*2)^3 = 8^3 = 512


the answer is the same as it should be because the formula is one of the properties of exponent arithmetic.


not let's look at 4^3 / 2^3.


this follows the form of a^x / b^x = (a/b)^x


we know that 4^3 / 2^3 is equal to 64 / 8 which is equal to 8.


we can use the formula as well to get:


4^3 / 2^3 is equal to (4/2)^3 is equal to 2^3 is equal to 8.


you get the same answer both ways as you should because the properties of exponent arithmetic tell you that you will.


so the rule is:


a^x * b^x = (a*b)^x


a^x / b^x = (a/b)^x