From the image, the task involves simplifying expressions with powers of 2. Let's simplify each of them step by step:

1. Expression:
   $\frac{2^5}{2^2}$
   Use the rule of exponents: $\frac{a^m}{a^n} = a^{m-n}$.
   Simplify:
   $2^{5-2} = 2^3$
   Final Answer: $2^3$.

2. Expression:
   $\frac{2^5}{2^3}$
   Simplify:
   $2^{5-3} = 2^2$
   Final Answer: $2^2$.

3. Expression:
   $\frac{2^5}{2^4}$
   Simplify:
   $2^{5-4} = 2^1$
   Final Answer: $2^1$ (or just $2$).

4. Expression:
   $\frac{2^5}{2^5}$
   Simplify:
   $2^{5-5} = 2^0$
   Recall that any number raised to the power 0 equals 1.
   Final Answer: $1$.

Final Results:

1. $2^3$
2. $2^2$
3. $2^1$
4. $1$

Would you like detailed explanations for any step? Let me know!

5 Related Questions:

1. What is the general rule for dividing exponents with the same base?
2. How do you simplify expressions involving negative exponents?
3. What happens when the numerator has a smaller exponent than the denominator?
4. Can the zero exponent rule apply to variables and not just numbers?
5. How can this concept be extended to fractions or decimals?

One Tip:

When working with exponents, always verify if the bases are the same before applying any exponent rules.