Question

Evaluate 4*81^-1/2 *(81^1/2+81^1/2)

Answer 1

$$\begin{gathered} 4\times {\left(81\right)}^{-\frac{1}{2}}\left[{\left(81\right)}^{\frac{1}{2}}+{\left(81\right)}^{\frac{1}{2}}\right] \\ =4\times {\left(9^2\right)}^{-\frac{1}{2}}\left[{\left(9^2\right)}^{\frac{1}{2}}+{\left(9^2\right)}^{\frac{1}{2}}\right] \\ =4\times {\left(9\right)}^{2\times -\frac{1}{2}}\left[9^{2\times \frac{1}{2}}+9^{2\times \frac{1}{2}}\right] \\ =4\times 9^{-1}\left[9+9\right] \\ =\frac{4}{9}\times 18 \\ =\frac{72}{9} \\ =8 \end{gathered}$$