document.write( "Question 384579: negative cube root of 7p/r^4 \n" ); document.write( "

Algebra.Com's Answer #272330 by jsmallt9(3758) $\"\"$ $\"About$

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$\"-root%283%2C+7p%2Fr%5E4%29\"$
\n" ); document.write( "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).

\n" ); document.write( "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:
\n" ); document.write( " $\"-root%283%2C+%287p%2Fr%5E4%29%28r%5E2%2Fr%5E2%29%29\"$
\n" ); document.write( " $\"-root%283%2C+7pr%5E2%2Fr%5E6%29\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"-root%283%2C+7pr%5E2%29%2Froot%283%2C+r%5E6%29\"$
\n" ); document.write( "And the denominator simplifies:
\n" ); document.write( " $\"-root%283%2C+7pr%5E2%29%2Fr%5E2%29\"$ \n" ); document.write( "

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