Question

2 to the power - n multipy 8 to the power 2n plus 1 multiply 16 to the power 2n devided by 4 to the power 3n = 1/16

Answer 1

$given \\ \frac{ {2}^{ - n} \times {8}^{2n + 1} \times {16}^{2n} }{ {4}^{3n} } = \frac{1}{16}$
$i.e. \\ \frac{ {2}^{ - n} \times {2}^{6n + 3} \times {2}^{8n} }{ {2}^{ 6n} } = {2}^{ - 4} \\ {2}^{ - n + 6n + 3 + 8n - 6n} = {2}^{ - 4} \\ {2}^{7n + 3} = {2}^{ - 4} \\ 7n + 3 = - 4 \\ n = - 1$