Final answer:
The expression simplifies to 16 by using exponent rules to multiply and subtract exponents, with the final step recognizing that 2^4 equals 16.
Step-by-step explanation:
The question presented is a mathematical expression involving the rules of exponents and division. To simplify the given expression ((2^5)^2 / 2^6 × 4), you apply the exponent rule that states when an exponent is raised to another exponent, you multiply the exponents. Hence, (2^5)^2 becomes 2^(5× 2) or 2^10. To proceed, divide the terms and subtract their exponents according to Division of Exponentials; (2^10 / 2^6) becomes 2^(10-6) which simplifies to 2^4. Lastly, since 2^2 equals 4, 2^4 can be further broken down as (2^2 × 2^2) or (4 × 4), which equals 16. Therefore, the numerator simplifies to 16. As there's no visible denominator in the given expression, the final result of the entire operation is just 16.