Show that $2^{n+5} + 2^{n+3} + 81(2^n)$ is a multiple of 11.

1. Express each term as a product involving $2^n$.

$2^{n+5} + 2^{n+3} + 81(2^n) = 2^n(2^5) + 2^n(2^3) + 81(2^n)$

2. Factor out $2^n$ and evaluate the numerical coefficient.

$= 2^n(32 + 8 + 81)$
$= 2^n(121)$

3. Conclude that the expression is a multiple of 11.

$= 11 \times 11(2^n)$
Since 121 is a multiple of 11, $2^{n+5} + 2^{n+3} + 81(2^n)$ is a multiple of 11.