(9x^3)^(5/2 )/ 27x^(-1/3)
=9^(5/2 ) (x^3)^(5/2 ) / (3^3)x^(-1/3)
=(3^5)(x^15/2 ) / (3^3)x^(-1/3)
=(3^2) x^(15/2 + 1/3 )
=9x^(47/6)
(9x^3)^(5/2 )/ 27x^(-1/3)
=9^(5/2 ) (x^3)^(5/2 ) / (3^3)x^(-1/3)
=(3^5)(x^15/2 ) / (3^3)x^(-1/3)
=(3^2) x^(15/2 + 1/3 )
=9x^(47/6)