Question

Find the value of (1³+ 2³+ 3³)^-3/2

Answer 1

$$\begin{gathered} {\left(1^3+2^3+3^3\right)}^{\frac{-3}{2}}={\left(1+8+27\right)}^{\frac{-3}{2}} \\ ={\left(36\right)}^{\frac{-3}{2}}={\left(6^2\right)}^{\frac{-3}{2}} \\ ={\left(6\right)}^{-3}={\left(\frac{1}{6}\right)}^3=\frac{1}{216}\mathrm{ANS}... \end{gathered}$$