Question

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Answer 1

(x⁻⁴ y^(2/3))^(-1/2) (x⁻(1/3) y⁻¹)^(1/2)
_____________________________
(x^(1/2) y³)^(-1/2) (x⁻(1/4) y⁻¹)^(1/3)

(x^(1/2) y³)^(1/2) (x⁻(1/3) y⁻¹)^(1/2)
= ____________________________
(x⁻⁴ y^(2/3))^(1/2) (x⁻(1/4) y⁻¹)^(1/3)

x^(1/4) y^(3/2) x⁻(1/3) y⁻(1/2)
= ______________________
x⁻² y^(1/3) x⁻(1/12) y⁻(1/3)

x^(1/4 - 1/3) y^(3/2 - 1/2)
=___________________
x^(-2 - 1/12) y^(1/3 - 1/3)
   
   x^(-1/12) y
= _________
   x^(-23/12)
= x^(-1/12 - (-23/12)) y
= x⁻² y
= y/x²