Question

Mark the correct alternative in the following question:

$$\begin{gathered} {\left(2^3\right)}^4= \\ \left(\mathrm{a}\right)2^{4^3}\left(\mathrm{b}\right)2^{3^4}\left(\mathrm{c}\right){\left(2^4\right)}^3\left(\mathrm{d}\right)\mathrm{None}\mathrm{of}\mathrm{these} \end{gathered}$$

Answer 1

Since,

$$\begin{gathered} {\left(2^3\right)}^4 \\ =2^{3\times 4}\left[\mathrm{As},{\left(x^m\right)}^n=x^{mn}\right] \\ =2^{4\times 3} \\ ={\left(2^4\right)}^3\left[\mathrm{As},x^{mn}={\left(x^m\right)}^n\right] \end{gathered}$$

Hence, the correct alternative is option (c).