Question

If (a^m)^n = a^m.a^n, find the value of :
m(n - 1) - (n - 1)​

Answer 1

Answer:

$( {a}^{m})^{n} = {a}^{m}. {a}^{n} \\ \implies \: {a}^{mn} = {a}^{m + n} \\ \implies \: mn \: = m + n...(1) \\ now \\ m(n - 1) - (n - 1) \\ = mn - m - n + 1 \\ = mn - (m + n) + 1 \\ = mn - mn + 1 ..( \because \: m + n = mn) \\ = 1 \\ thus \\ m(n - 1) - (n - 1) = 1$