This is a question from an exam on calculus.
$$ \lim\_{x \rightarrow \infty }(-6e^{11x} + 9sin(x) + 3e^{8x} )^{8/4x} $$

I tried this:

$$ (3e^{(8x)})^{(8/4x)} < (-6e^{11x} + 9sin(x) + 3e^{8x} )^{8/4x} < (3e^{8x}+3e^{8x}+3e^{8x} )^{8/4x} $$

However, I'm not sure if it's right.
The problem is:
$ (3e^{(8x)})^{(8/4x)} < (-6e^{11x} + 9sin(x) + 3e^{8x} )^{8/4x} $

If it was $+6e$ instead of $-6e$,then I am sure that it's true, because it's make sense that the middle expression is bigger, because the middle expression is the same like the left side , only with more additions. but...

There is a minus on the middle expression, how can I know that
$ (3e^{(8x)})^{(8/4x)} < (-6e^{11x} + 9sin(x) + 3e^{8x} )^{8/4x} $ is really true?

Can I use the squeeze theorem on this exercise?