Question

if m and n are two natural numbers and mⁿ = 81. Then the value of n^mn is

Answer 1

$$\begin{gathered} \mathrm{As}\mathrm{we}\mathrm{know}\mathrm{that} \\ 81=3\times 3\times 3\times 3=3^4 \\ \mathrm{So}81=3^4={\mathrm{m}}^{\mathrm{n}} \\ \mathrm{SO}\mathrm{we}\mathrm{get}, \\ \mathrm{m}=3\mathrm{and}\mathrm{n}=4 \\ \mathrm{So}\mathrm{n}{}^{\mathrm{mn}}=4^{3\times 4}=4^{12} \end{gathered}$$