SOLUTION: how do you solve (6x^(-1/3)+2x^5/3)/2x^-4/3

Question 220109: how do you solve
(6x^(-1/3)+2x^5/3)/2x^-4/3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First let's reduce the fraction. Reduced fractions are usually easier to work with. Since 2 is a common factor we can reduce the fraction be a factor of 2:

From this point there are, as usual, a number of ways we can go. The most direct way to the answer is to multiply the numerator and denominator by . (I hope you can see that this will turn the denominator into a 1 which, in turn, means that we will no longer have a fraction. And not having a fraction anymore is, I hope you agree, a good thing.):

In the denominator, since

the rule for exponents when you multiply is to add the exponents, and
-4/3 + 4/3 = 0, and

the denominator becomes a 1!

Now let's simplify using the Distributive Property:

Again we'll use the "add the exponents when multiplying" rule:

And we're finished!
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