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Решите задачу:

$x ^{ \frac{1}{2} }-y ^{ \frac{1}{2} } =(x ^{ \frac{1}{6} }) ^{3} -(y ^{ \frac{1}{6} }) ^{3}=(x ^{ \frac{1}{6} } -y ^{ \frac{1}{6} })(x ^{ \frac{1}{3} }+x ^{ \frac{1}{6} }y ^{ \frac{1}{6} } +y ^{ \frac{1}{3} })\\\\ x ^{ \frac{1}{4} }-y ^{ \frac{1}{4} }=(x ^{ \frac{1}{12} } ) ^{3}-(y ^{ \frac{1}{12} } ) ^{3}=(x ^{ \frac{1}{12} } -y ^{ \frac{1}{12} })(x ^{ \frac{1}{6} }+x ^{ \frac{1}{12} }y ^{ \frac{1}{12} }+y ^{ \frac{1}{6} } )\\\\x ^{ \frac{1}{3} }-y ^{ \frac{1}{3} }= (x ^{ \frac{1}{9} }) ^{3} -(y ^{ \frac{1}{9} }) ^{3}=(x ^{ \frac{1}{9} }-y ^{ \frac{1}{9} })(x ^{ \frac{2}{9} }+x ^{ \frac{1}{9} }y ^{ \frac{1}{9} }+y ^{ \frac{2}{9} })$