-8{-2-3[5-2(1-3)+4(8-10)]}+3[2-5(1-3)-10]

Let's solve the expression step by step:

Given expression:
\[
-8\{-2-3[5-2(1-3)+4(8-10)]\}+3[2-5(1-3)-10]
\]

### Step 1: Simplify the innermost parentheses.

1. **Simplify \(1 - 3\):**
   \[
   1 - 3 = -2
   \]

2. **Simplify \(8 - 10\):**
   \[
   8 - 10 = -2
   \]

So the expression becomes:
\[
-8\{-2-3[5-2(-2)+4(-2)]\}+3[2-5(-2)-10]
\]

### Step 2: Distribute and simplify the expressions inside the brackets.

1. **Simplify \(2(-2)\):**
   \[
   2(-2) = -4
   \]

2. **Simplify \(4(-2)\):**
   \[
   4(-2) = -8
   \]

So the expression becomes:
\[
-8\{-2-3[5 - (-4) - 8]\}+3[2 - 5(-2) - 10]
\]

### Step 3: Simplify further within the brackets.

1. **Simplify \(5 - (-4)\):**
   \[
   5 - (-4) = 5 + 4 = 9
   \]

2. **Simplify \(9 - 8\):**
   \[
   9 - 8 = 1
   \]

3. **Simplify \(5(-2)\):**
   \[
   5(-2) = -10
   \]

So the expression becomes:
\[
-8\{-2-3(1)\} + 3[2 - (-10) - 10]
\]

### Step 4: Distribute and simplify.

1. **Simplify \(3(1)\):**
   \[
   3(1) = 3
   \]

So the expression becomes:
\[
-8\{-2-3\} + 3[2 + 10 - 10]
\]

2. **Simplify \(-2 - 3\):**
   \[
   -2 - 3 = -5
   \]

So the expression becomes:
\[
-8(-5) + 3[2 + 10 - 10]
\]

3. **Simplify \(2 + 10 - 10\):**
   \[
   2 + 10 - 10 = 2
   \]

So the expression becomes:
\[
-8(-5) + 3(2)
\]

### Step 5: Final calculations.

1. **Simplify \(-8(-5)\):**
   \[
   -8(-5) = 40
   \]

2. **Simplify \(3(2)\):**
   \[
   3(2) = 6
   \]

So the final expression becomes:
\[
40 + 6 = 46
\]

The final answer is:
\[
\boxed{46}
\]

Would you like more details on any part of the solution or have any questions?

---

Here are 5 related questions to expand on the concept:

1. How do you simplify nested parentheses in a mathematical expression?
2. What is the order of operations, and why is it important?
3. How do negative numbers affect multiplication and addition in expressions?
4. How would you solve a similar expression with more variables involved?
5. How can you verify your result when solving complex arithmetic expressions?

**Tip:** Always start by simplifying the innermost parentheses first when dealing with complex expressions. This makes it easier to reduce the problem step by step.

Learn how to solve a complex arithmetic expression involving nested parentheses step-by-step. This problem covers arithmetic operations, simplification of nested parentheses, and adheres to the order of operations. Suitable for students in Grades 6-8.

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