We are tasked with solving the following expression:

$\frac{2^9 \times 2^{-2}}{2^4}$

Step-by-Step Solution:

1. Combine the exponents in the numerator: $2^9 \times 2^{-2} = 2^{9 + (-2)} = 2^{7}$ This simplifies the expression to: $\frac{2^7}{2^4}$

2. Simplify the fraction using the properties of exponents (i.e., subtract the exponents when dividing like bases): $\frac{2^7}{2^4} = 2^{7 - 4} = 2^3$

3. Calculate the value of $2^3$: $2^3 = 8$

Final Answer:

$\boxed{8}$

Would you like further details or explanations on any part of this solution?

Related Questions:

1. How do you simplify expressions with different bases?
2. What are the properties of exponents used in simplifying powers?
3. How can you simplify expressions with negative exponents?
4. What happens when you divide numbers with exponents and the same base?
5. What are the steps for solving a complex exponentiation problem?

Tip:

When multiplying or dividing exponential terms with the same base, remember to add or subtract the exponents as appropriate!