If $(a^{m n}) = a^{m} - a^{n}$ , find the value of $m (n - 1) - (n - 1)$ .

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Solution

The correct option is A $1$
$a^{m n} = a^{m} + a^{n}$

Taking log both sides
$m n log a = m log a + n log a \Rightarrow m n = m + n . . . . . . . . . (1)$

So, $m (n - 1) - (n - 1) = m n - m - n + 1 = m n - (m + n) + 1 = 0 + 1 = 1$

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