Math Problem Statement
(2^2 · 2^3 - 3^3)^6 ÷ 5^5 + 4 · 3^2 - 5 · 2^3
Solution
Let's analyze and solve the given mathematical expression from the image.
The expression is:
Step-by-step solution:
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Simplify inside the parentheses: So,
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Apply the exponentiation:
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Divide by :
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Calculate the rest of the terms:
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Final expression:
Final Answer:
The value of the given expression is .
Would you like more details or have any questions?
Here are 5 related questions to deepen understanding:
- How do we simplify products of powers with the same base?
- What is the rule for dividing exponents with the same base?
- How do exponent laws apply when simplifying more complex expressions?
- What are some shortcuts for calculating higher powers of small numbers?
- How do we handle expressions with multiple operations (exponents, multiplication, and division)?
Tip: Always simplify expressions inside parentheses first before applying powers and other operations.
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Math Problem Analysis
Mathematical Concepts
Exponents
Order of Operations
Simplification
Formulas
a^m · a^n = a^(m+n)
Exponentiation: (a)^n
Basic arithmetic: addition, subtraction, multiplication
Theorems
Laws of Exponents
Order of Operations (PEMDAS)
Suitable Grade Level
Grades 9-10