https://file.aiquickdraw.com/mathbot/file/174097616451684vw5uiz.jpg

The image you uploaded shows a complex mathematical expression. Let's break it down and solve it step by step.

The expression given is:

\[
\sqrt{
\frac{1}{5} + \frac{3}{2} + 10^{-1} \ \  \  + \ 3^{-2} \left( \frac{1}{5} \right)^{-2} + \left( \frac{1}{3} \right)^{2} + \frac{3 - 1}{3}  + 2 \cdot \left( -2 - ( - 5)^2 \right)^3
}
\]

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.

Resuelva la siguiente expresión sin borrar cálculos, en orden y limpieza.

This problem involves solving a complex expression with exponents and square roots. The solution steps break down the expression using algebraic rules and the properties of complex numbers, particularly focusing on handling negative numbers inside square roots. Suitable for students in Grades 10-12.

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