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$\frac{6 {(8)}^{n + 1} + 16 {(2)}^{3 n - 2}}{10 {(2)}^{3 n + 1} - 7 {(8)}^{n}} =$

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answer is D.

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Detailed Solution

$\frac{6 {(8)}^{n + 1} + 16 {(2)}^{3 n - 2}}{10 {(2)}^{3 n + 1} - 7 {(8)}^{n}}$

$= \frac{6 {(2^{3})}^{n + 1} + 16 {(2)}^{3 n - 2}}{10 {(2)}^{3 n + 1} - 7 {(2^{3})}^{n}}$

$= \frac{6 \times 2^{3 n + 3} + 16 {(2)}^{3 n - 2}}{10 {(2)}^{3 n + 1} - 7 \times 2^{3 n}}$

$= \frac{6 \times 2^{3 n} \times 2^{3} + 16 \times 2^{3 n} \times 2^{- 2}}{10 \times 2^{3 n} \times 2 - 7 \times 2^{3 n}}$

$= \frac{2^{3 n} (6 \times 2^{3} + 16 \times 2^{- 2})}{2^{3 n} (10 \times 2 - 7)}$

$= \frac{6 \times 8 + 16 \times \frac{1}{4}}{20 - 7}$

$= \frac{52}{13}$

$= 4$

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