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

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Simplify the expression by following steps:
- step0: Solution:
  $$\frac{3^{y+4}}{3^{y}}$$
- step1: Multiply by $$a^{-n}:$$
  $$3^{y+4}	imes 3^{-y}$$
- step2: Multiply:
  $$3^{y+4-y}$$
- step3: Calculate:
  $$3^{4}$$
- step4: Evaluate the power:
  $$81$$
Calculate or simplify the expression $$ \frac{3 \cdot 2^{r}-}{2^{r}}- $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{3	imes 2^{r}}{2^{r}}$$
- step1: Multiply by $$a^{-n}:$$
  $$3	imes 2^{r}	imes 2^{-r}$$
- step2: Multiply the terms:
  $$3	imes 2^{r-r}$$
- step3: Subtract the terms:
  $$3	imes 2^{0}$$
- step4: Evaluate the power:
  $$3$$
Calculate or simplify the expression $$ \frac{5^{2-x}-2}{5^{-x}+2} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{5^{2-x}-2}{5^{-x}+2}$$
- step1: Rewrite the expression:
  $$\frac{25\left(5^{x}ight)^{-1}-2}{\left(5^{x}ight)^{-1}+2}$$
- step2: Rewrite the expression:
  $$\frac{\frac{25-2	imes 5^{x}}{5^{x}}}{\left(5^{x}ight)^{-1}+2}$$
- step3: Rewrite the expression:
  $$\frac{\frac{25-2	imes 5^{x}}{5^{x}}}{\frac{1+2	imes 5^{x}}{5^{x}}}$$
- step4: Multiply by the reciprocal:
  $$\frac{25-2	imes 5^{x}}{5^{x}}	imes \frac{5^{x}}{1+2	imes 5^{x}}$$
- step5: Reduce the fraction:
  $$\left(25-2	imes 5^{x}ight)	imes \frac{1}{1+2	imes 5^{x}}$$
- step6: Multiply the terms:
  $$\frac{25-2	imes 5^{x}}{1+2	imes 5^{x}}$$
Here are the simplified results for each expression:

e) For the expression $$ \frac{3^{y+4}}{3^{y}} $$:
- This simplifies to $$ 3^{(y+4) - y} = 3^{4} = 81 $$.

g) For the expression $$ \frac{3 \cdot 2^{r}-}{2^{r}}- $$:
- This simplifies to $$ 3 $$.

i) For the expression $$ \frac{5^{2-x}-2}{5^{-x}+2} $$:
- This simplifies to $$ \frac{25 - 2 \cdot 5^{x}}{1 + 2 \cdot 5^{x}} $$.

If you have any further questions or need additional assistance, feel free to ask!
e) $$ 81 $$ g) $$ 3 $$ i) $$ \frac{25 - 2 \cdot 5^{x}}{1 + 2 \cdot 5^{x}} $$

e)
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