If $2^{n - m} = 16$ and $3^{n + m} = 729$ then $m n = ?$

5

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4

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6

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None of the above.

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Solution

The correct option is C $5$
$2^{n - m} = 16 2^{n - m} = 2^{4} n - m = 4 \dots (1) 3^{n + m} = 729 3^{n + m} = 3^{6} n + m = 6 \dots (2) (1) + (2) 2 n = 10 n = 5 m = 1$
$n m = 5 . . . A n s w e r$

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