Respuesta :
Fourth root of 128x^7 y^7
= ⁴√(128x⁷y⁷)
We would then expand (128x⁷y⁷)
= ⁴√(2*2*2*2*2*2*2*x*x*x*x*x*x*x*y*y*y*y*y*y*y)
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.
= (2*x*y) ⁴√(2*2*2*x*x*x*y*y*y)
= (2*x*y) ⁴√(8x³y³)
= 2xy ⁴√(8x³y³)
Note the 4 is associated with the radical sign which covers 8x³y³
We would then expand (128x⁷y⁷)
= ⁴√(2*2*2*2*2*2*2*x*x*x*x*x*x*x*y*y*y*y*y*y*y)
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.
= (2*x*y) ⁴√(2*2*2*x*x*x*y*y*y)
= (2*x*y) ⁴√(8x³y³)
= 2xy ⁴√(8x³y³)
Note the 4 is associated with the radical sign which covers 8x³y³