The question asks to simplify the expression $4^7 \times 4^{-5}$.

We can apply the rule of exponents:

$a^m \times a^n = a^{m+n}$

In this case, we have the same base (4), so we can add the exponents:

$4^7 \times 4^{-5} = 4^{7 + (-5)} = 4^2$

Thus, the expression simplifies to $4^2$, which matches option B.

Would you like more details, or do you have any questions? Here are some follow-up questions:

1. What are the general rules for multiplying exponents with the same base?
2. How would the answer change if the base numbers were different?
3. Can you apply this rule when dividing exponents with the same base?
4. What happens if one of the exponents is zero?
5. How do negative exponents affect the result?

Tip: When multiplying powers with the same base, always remember to add the exponents.