Question

Find the value of ${16}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$

Answer 1

Finding the value of ${16}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$

We can rewrite it as ${\left(2^4\right)}^{1/4}$

$\begin{array}{rcl}{\left(2^4\right)}^{1/4}& =& 2^{4\times 1/4}\end{array}$ ; $[{\because \left(a^m\right)}^n=a^{m\times n}]$

$\begin{array}{rcl}& =& 2^{4/4}\\ & =& 2\end{array}$

Hence the value of ${16}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\mathrm{is}2$