Question

find the value of n^m+n if m^n = 32 where m &n are positive integers​

Answer 1

Doing the Prime Factorization of 32, We get

$32 = 2 \times 2 \times 2 \times 2 \times 2 \\ 32 = {2}^{5}$

Therefore,

${m}^{n} = {2}^{5}$

By Comparing,

m = 2

n = 5

Hence,

${n}^{m + n} = {5}^{2 + 5} = {5}^{7}$