We are asked to simplify the expression:

$\frac{(2^5)^3 \cdot 2^{-7}}{2^{-6}}$

Step-by-step simplification:

1. Simplify the numerator:
   Use the property of exponents: $(a^m)^n = a^{m \cdot n}$.
   So, $(2^5)^3 = 2^{5 \cdot 3} = 2^{15}$.
   Therefore, the numerator becomes:
   $2^{15} \cdot 2^{-7}$

2. Combine the terms in the numerator:
   Use the rule $a^m \cdot a^n = a^{m+n}$.
   So,
   $2^{15} \cdot 2^{-7} = 2^{15 + (-7)} = 2^{8}$

3. Simplify the denominator:
   The denominator is $2^{-6}$.

4. Now simplify the entire fraction:
   $\frac{2^8}{2^{-6}}$ Use the rule $\frac{a^m}{a^n} = a^{m-n}$.
   So,
   $\frac{2^8}{2^{-6}} = 2^{8 - (-6)} = 2^{8 + 6} = 2^{14}$

Thus, the simplified expression is:

$2^{14}$

Final Answer:

The correct answer is d.) $2^{14}$.

Would you like a more detailed explanation, or do you have any questions?

Related questions to explore:

1. How do you simplify expressions involving negative exponents?
2. What happens when you divide two powers with the same base?
3. What is the rule for multiplying powers of the same base?
4. How can you apply the laws of exponents to solve more complex expressions?
5. How do you express a number in scientific notation using exponents?

Tip:

When dealing with exponents, always remember to combine powers of the same base before simplifying fractions.