Question

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

Answer 1

(a^m)ⁿ = a^m .aⁿ
⇒ a^mn = a^{m + n}
⇒ mn = m + n               ....(1)
Now,
m( n - 1 ) - ( n - 1 )
= mn - m - n + 1
= m + n - m - n + 1      ....[ From (1) ]
= 1