Math Problem Statement
2/(3π⋅7,5⋅10^(-2) )⋅6⋅10^(-10)⋅100⋅(1+0,25)[(1+0,25)^3-0,25^3 ]/(1+2⋅0,25)^2
Solution
Let's break down the given expression step by step:
Step 1: Simplify the constants and expressions inside the brackets
- First, calculate the values inside the parentheses:
Now substitute the values back into the expression:
- Simplify the subtraction inside the brackets:
So the expression becomes:
Step 2: Simplify the denominator
Now, calculate the term in the denominator:
Now substitute this into the expression:
Step 3: Simplify the remaining expression
We can now focus on simplifying the remaining constants:
- The numerator constants:
Now, let's calculate:
Numerator:
So the numerator is .
Denominator:
Now divide by :
Step 4: Final calculation
Now, let's finish by dividing the numerator by the denominator:
Final Answer:
Would you like any further details or clarifications on specific steps?
Here are some related questions to explore:
- How does the value of affect the final result?
- What happens if the power of 10 in the expression changes?
- How would you approach simplifying an expression with both exponents and trigonometric functions?
- How does the distributive property apply when simplifying terms with multiple factors?
- What are some methods for estimating large and small numbers effectively?
Tip: When dealing with complex expressions involving exponents, always try to simplify each part step-by-step to avoid errors in calculation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponents
Parentheses and Order of Operations
Formulas
Exponentiation rules
Order of operations (PEMDAS)
Basic arithmetic operations
Theorems
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Suitable Grade Level
Grades 9-11
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