Question

Fourth root of 128x^7 y^7

Answer 1

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

Answer 2

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


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