Apartado a
Podemos simplificar de la siguiente manera: (2x2/3)3(4x−1/3)2=23(x2/3)342(x−1/3)2=\frac{(2x^{2/3})^3} {(4x^{−1/3})^2}= \frac{2^3(x^{2/3})^3}{4^2(x^{−1/3})^2}= (4x−1/3)2(2x2/3)3=42(x−1/3)223(x2/3)3= =8x216x−2/3=x2x2/32=x8/32=\frac{8x^2}{16x^{−2/3}}=\frac{x^2 x^{2/3}}{2} =\frac{x^{8/3}}{2}=16x−2/38x2=2x2x2/3=2x8/3
Apartado b
(x3y−1)2(xy2)−2=(x3)2(y−1)2x−2(y2)−2=x6y−2x−2y−4=x6x2y−2y4=x8y2\frac{(x^3y^{−1})^2}{(xy^2)^{−2}}=\frac{(x^3)^2(y^{−1})^2}{x^{−2}(y^2)^{−2}}=\frac{x^6y^{−2}} {x^{−2}y^{−4}}=x^6x^2y^{−2}y^4=x^8y^2(xy2)−2(x3y−1)2=x−2(y2)−2(x3)2(y−1)2=x−2y−4x6y−2=x6x2y−2y4=x8y2