How to calculate $\lim\limits_{i\to\infty} \frac{5^i - 2^{3i+1}}{7^{i-2}+8^i}$? I'm having trouble finding the answer to the limit 
$$\lim\limits_{i\to\infty} \dfrac{5^i - 2^{3i+1}}{7^{i-2}+8^i}$$

I get the answer 98, which to me seem to be wrong. Can someone help me?
Thanks in advance.

Hint. One may write, as $i \to \infty$,
$$
a_i = \frac{5^i - 2^{3i+1}}{7^{i-2}+8^i}=\frac{2^{3i}}{8^i}\cdot\frac{(5/8)^i - 2}{\frac1{49}(7/8)^{i}+1}.
$$
