Evaluate the following :

$(27)^{\dfrac{4}{3}} + (32)^{0.8} + (0.8)^{-1} + (0.8)^0$

Given,

$(27)^{\dfrac{4}{3}} + (32)^{0.8} + (0.8)^{-1} + (0.8)^0$

Simplifying the expression :

$\Rightarrow (27)^{\dfrac{4}{3}} + (32)^{0.8} + (0.8)^{-1} + (0.8)^0 \\[1em] \Rightarrow [(3)^3]^{\dfrac{4}{3}} + [(2)^5]^{0.8} + \Big(\dfrac{8}{10}\Big)^{-1} + 1 \\[1em] \Rightarrow (3)^{3 \times \dfrac{4}{3}} + [(2)^5]^{0.8} + \Big(\dfrac{8}{10}\Big)^{-1} + 1 \\[1em] \Rightarrow (3)^4 + (2)^4 + \Big(\dfrac{10}{8}\Big)^{1} + 1 \\[1em] \Rightarrow 81 + 16 + \dfrac{10}{8} + 1 \\[1em] \Rightarrow 97 + 1.25 + 1 \\[1em] \Rightarrow 99.25$

Hence, $(27)^{\dfrac{4}{3}} + (32)^{0.8} + (0.8)^{-1} + (0.8)^0 = 99.25$.