Question

if the value of (m)ⁿ = 32, where m and n are two positive integers, then what is the value of (n)^mn

Answer 1

$$\begin{gathered} \mathrm{After}\mathrm{factorizing}32\mathrm{we}\mathrm{get}, \\ 32=2\times 2\times 2\times 2\times 2=2^5 \\ \mathrm{So}\mathrm{comparing}\mathrm{it}\mathrm{with}{\mathrm{m}}^{\mathrm{n}}=32\mathrm{we}\mathrm{get}, \\ \mathrm{m}=2\mathrm{and}\mathrm{n}=5 \\ \mathrm{So}{\mathrm{n}}^{\mathrm{mn}}=5^{5\times 2}=5^{10} \end{gathered}$$