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 .
Do you need further details or clarification on this?
Here are five related questions you might find useful:
- How are exponents handled when multiplying or dividing terms with the same base?
- How can we simplify expressions involving powers of two?
- What are some common properties of exponents and logarithms?
- Can expressions like this be solved by factoring first before simplifying?
- 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