document.write( "Question 203101This question is from textbook
\n" ); document.write( ": {{cube root of 108x^3y^7/2y^3}} \n" ); document.write( "
Algebra.Com's Answer #153237 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"root%283%2C+%28108x%5E3%2Ay%5E7%29%2F%282y%5E3%29%29\"
\n" ); document.write( "Let's start by reducing the fraction inside:
\n" ); document.write( "
\n" ); document.write( "Now we look for perfect cube factors:
\n" ); document.write( "
\n" ); document.write( "Now we can use one of the properties of roots (which apply for all roots: square, cube, 4th, 5th, etc.): \"sqrt%28x%2Ay%29+=+sqrt%28x%29%2Asqrt%28y%29\". This allows us to separate factors in a root into separate roots:
\n" ); document.write( "
\n" ); document.write( "Now we can simplify the cube roots of the perfect cubes:
\n" ); document.write( "
\n" ); document.write( "Using the Commutative Property of multiplication to rearrange the order:
\n" ); document.write( "
\n" ); document.write( "And finally, using the same property of roots as earlier (except in reverse), to combine the cube roots:
\n" ); document.write( "\"3xy%2Aroot%283%2C+2%29%2Aroot%283%2C+y%29+=+3xy%2Aroot%283%2C+2y%29\" \n" ); document.write( "
\n" );