Math Problem Statement
Solution
The image you uploaded shows a complex mathematical expression. Let's break it down and solve it step by step.
The expression given is:
\frac{1}{5} + \frac{3}{2} + 10^{-1} \ \ \ + \ 3^{-2} \left( \frac{1}{5} \right)^{-2} + \left( \frac{1}{3} \right)^{2} + \frac{3 - 1}{3} + 2 \cdot \left( -2 - ( - 5)^2 \right)^3 }$$ I'll begin by simplifying each part of the expression. Let me perform the calculations to present you with a detailed solution. sympy as sp # Define the terms term1 = 1/5 + 3/2 + 10**(-1) # First part term2 = 3**(-2) * (1/5)**(-2) # Second part term3 = (1/3)**2 # Third part term4 = (3 - 1)/3 # Fourth part term5 = 2 * (-2 - (-5)**2)**3 # Fifth part # Add all the terms together expression = term1 + term2 + term3 + term4 + term5 # Take the square root of the entire expression result = sp.sqrt(expression) # Simplify the result simplified_result = sp.simplify(result) simplified_resultThe result of the expression is a complex number: $$198.395172432306i$$ This means that the expression evaluates to an imaginary value due to the presence of negative values inside the square root. Would you like me to explain any specific steps in the solution, or do you have any other questions? Here are some related questions for you: 1. How do complex numbers arise in square roots of negative numbers? 2. Can we modify the expression to avoid a complex solution? 3. What are the real-number solutions for similar types of problems? 4. How do we simplify expressions with fractional exponents? 5. What are other ways to approach complex numbers in mathematics? **Tip:** To prevent imaginary numbers, always check the values under square roots or other even exponents to ensure they are positive before simplifying.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponentiation
Square Roots
Complex Numbers
Order of Operations
Formulas
Exponentiation rules (a^m * a^n = a^(m+n))
Square root properties (√(a * b) = √a * √b)
Complex number operations
Theorems
Rules for simplifying fractional exponents
Properties of square roots of negative numbers
Suitable Grade Level
Grades 10-12
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