To evaluate the given expression:

$\frac{2^3 \times 2^{-3}}{2^2}$

Step-by-Step Solution:

1. Simplify the numerator $2^3 \times 2^{-3}$:

   • Use the property of exponents: $a^m \times a^n = a^{m+n}$.
   • $2^3 \times 2^{-3} = 2^{3 + (-3)} = 2^0$.

2. Simplify $2^0$:

   • By definition, any non-zero number raised to the power of $0$ is $1$.
   • So, $2^0 = 1$.

3. Divide the numerator by $2^2$:

   • The expression becomes: $\frac{1}{2^2}$.
   • Simplify $2^2 = 4$.

4. Final result: $\frac{1}{4}$

Final Answer:

$\frac{1}{4}$

Would you like further clarification or have questions? Here are related questions to explore further:

1. What are the general laws of exponents, and how are they applied in similar problems?
2. Why does $a^0 = 1$ hold true for any non-zero number $a$?
3. How can you interpret this result in real-world applications, such as scaling factors?
4. How do negative exponents relate to fractions, e.g., $a^{-n} = \frac{1}{a^n}$?
5. Can this problem be extended to expressions with variables like $\frac{x^m \cdot x^{-n}}{x^p}$?

Tip: Always simplify exponents step-by-step, applying rules consistently to avoid mistakes!