Math Problem Statement

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

Solution

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

Do you need further details or clarification on this?

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.

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Math Problem Analysis

Mathematical Concepts

Exponents
Order of Operations
Algebra

Formulas

Exponentiation: a^m ∙ a^n = a^(m+n)
Division of exponents: a^m : a^n = a^(m-n)
Order of Operations: PEMDAS/BODMAS
Simplification: (a ∙ b)^n = a^n ∙ b^n

Theorems

Properties of Exponents
Order of Operations Theorem

Suitable Grade Level

Grades 9-12