Question

4 * 81^-1/2 * 81^1/2 + 81 ^3/2

Answer 1

$$\begin{gathered} 4\times {\left(81\right)}^{-1/2}\times {\left(81\right)}^{1/2}+{\left(81\right)}^{3/2} \\ =4\times {\left[9^2\right]}^{-1/2}\times {\left[9^2\right]}^{1/2}+{\left[9^2\right]}^{3/2} \\ =4\times {\left(9\right)}^{-1}\times {\left(9\right)}^1+{\left(9\right)}^3\left[\mathbf{as}\mathbf{,}\mathbf{}{\left({\mathbf{a}}^{\mathbf{m}}\right)}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{mn}}\right] \\ =4\times \frac{1}{9}\times 9+729\mathbf{}\mathbf{}\mathbf{}\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{-}\mathbf{m}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{{\mathbf{a}}^{\mathbf{m}}}\right] \\ =4+729 \\ =733 \end{gathered}$$