SOLUTION: negative cube root of 7p/r^4

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Question 384579: negative cube root of 7p/r^4
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
-root%283%2C+7p%2Fr%5E4%29
I assume we are supposed to simplify the expression. With radical expressions part of simplifying is to rationalize denominators (which includes eliminating fractions within a radical).

With a fraction inside the radical I like to start by multiplying the numerator and denominator of the fraction what whatever it takes to create a denominator that is a power of the type of root. This is a cube root so we want the denominator to become a perfect cube. The "nearest" perfect cube is r%5E6. So:
-root%283%2C+%287p%2Fr%5E4%29%28r%5E2%2Fr%5E2%29%29
-root%283%2C+7pr%5E2%2Fr%5E6%29
Now we can use a property of radicals, root%28a%2C+p%2Fq%29+=+root%28a%2C+p%29%2Froot%28a%2C+q%29, to split the numerator and denominator into separate radicals:
-root%283%2C+7pr%5E2%29%2Froot%283%2C+r%5E6%29
And the denominator simplifies:
-root%283%2C+7pr%5E2%29%2Fr%5E2%29