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The simplified result of the given mathematical expression is approximately \(-3.963\).

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Here are five related questions you might find useful:
1. How are exponents handled when multiplying or dividing terms with the same base?
2. How can we simplify expressions involving powers of two?
3. What are some common properties of exponents and logarithms?
4. Can expressions like this be solved by factoring first before simplifying?
5. How can you verify the result of an expression like this manually?

**Tip:** When simplifying expressions with exponents, always apply the laws of exponents step by step to avoid errors.

(2^8 : 2^6 - 2)² - (2³ ∙ 5²)² : 2¹⁴ + (125² ∙ 5⁴ - 5 ∙ 2²)² - 2¹⁶ : (2³)⁴

Learn how to simplify the complex mathematical expression involving powers and exponents: (2^8 : 2^6 - 2)² - (2³ ∙ 5²)² : 2¹⁴ + (125² ∙ 5⁴ - 5 ∙ 2²)² - 2¹⁶ : (2³)⁴. This problem involves understanding key algebraic concepts such as the properties of exponents, division, and multiplication rules. Suitable for high school students in Grades 9-12.

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