Question

Mark the correct alternative in the following question:

$$\begin{gathered} {\left(1+3+5+7+9+11\right)}^{\frac{3}{2}}= \\ \left(\mathrm{a}\right)36\left(\mathrm{b}\right)216\left(\mathrm{c}\right)256\left(\mathrm{d}\right)\mathrm{None}\mathrm{of}\mathrm{these} \end{gathered}$$

Answer 1

Since,

$$\begin{gathered} {\left(1+3+5+7+9+11\right)}^{\frac{3}{2}} \\ ={\left(36\right)}^{\frac{3}{2}} \\ ={\left(6^2\right)}^{\frac{3}{2}} \\ =6^{2\times \frac{3}{2}}\left[\mathrm{As},{\left(x^m\right)}^n=x^{mn}\right] \\ =6^3 \\ =216 \end{gathered}$$

Hence, the correct alternative is option (b).