\(\left[\dfrac{1}{216}\right]^{-2/3} = 216^{2/3} = (6^3)^{2/3} = 6^2 = 36\)
\(\left[\dfrac{1}{27}\right]^{-4/3} = 27^{4/3} = (3^3)^{4/3} = 3^4 = 81\)
Sum \(= 36 + 81 = 117\). Note: The answer key states \(\dfrac{3}{4}\). Students should verify the original expression carefully as printed; the exponents may differ from what appears here.