How to simplify this expression that contains exponential terms?

Question

In a multiple choice exam , I encountered the following question. The answer to the question is $$ \frac{17}{8}.$$

The question is:

$$\frac{16^{x+1}+4^{2x}}{2^{x-3}8^{x+2}} \text{ is ? }$$

Answer 1

Hint:

Write the terms in the fraction in a common base: $2$

$4 = 2^2,\; 8 = 2^3,\;16 = 2^4$.

$$\frac{(2^4)^{x+1}+(2^2)^{2x}}{2^{x-3}(2^3)^{x+2}}$$

Then use the fact that $(a^b)^c = a^{bc}$, and follow by factoring. You'll also want to remember that $a^na^m = a^{n + m}$.