Verified Answer :

128^1/4 x^7/4 y^7/4


i need 20 letters, stil  not enough

olemakpadu

Fourth root of 128x^7 y^7
= ⁴√(128x⁷y⁷)

We would then expand (128x⁷y⁷)

                                     = ⁴√(2222222xxxxxxxyyyyyyy)

For every four 2's we bring out one 2 out of the radical, and for every four x's and four y's we bring out one x and one y out of the radical.
              
                                    = (2xy)   ⁴√(222xxxyyy)

                                    = (2xy)    ⁴√(8x³y³)
                                              
                                   = 2xy  ⁴√(8x³y³)
                               
Note the 4 is associated with the radical sign which covers 8x³y³

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