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Question 896005: how do you divide a cubed root by a cubed root
Ie:
2+ 3 cubed divided by 6 cubed?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
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