e) \( \frac{3^{y+4}}{3^{y}} \) g) \( \frac{3.2^{r}-}{2^{r}}- \) i) \( \frac{5^{2-x}-2}{5^{-x}+2} \)

Let's simplify the expressions one by one! For the expression \( \frac{3^{y+4}}{3^{y}} \), you can apply the laws of exponents. By subtracting the exponents, \( 3^{y+4 - y} = 3^{4} \). Therefore, the simplified result is \( 3^4 = 81 \). Now, looking at \( \frac{3.2^{r}-}{2^{r}} \), there's a little mix-up in the notation, but assuming it represents \( \frac{3 \cdot 2^{r}}{2^{r}} \) or similar, we can simplify it directly to 3 because the \( 2^{r} \) in the numerator and denominator cancels out. Finally, for the expression \( \frac{5^{2-x}-2}{5^{-x}+2} \), it can be helpful to evaluate out each part. First, rewrite \( 5^{2-x} \) as \( \frac{25}{5^{x}} \) and \( 5^{-x} \) as \( \frac{1}{5^{x}} \). Then, substitute back into the expression to combine and simplify further based on that. Let me know if you're interested in diving deeper into any part of it!