https://file.aiquickdraw.com/mathbot/file/1727272538288qyy7auss.jpg

The problem you've uploaded is:

\[
\frac{11^3 - 8 \cdot (31 - 12 + 9)}{41 \cdot 3^3}
\]

Let's break this down step by step.

### Step 1: Calculate \(11^3\)
\[
11^3 = 11 \times 11 \times 11 = 1331
\]

### Step 2: Simplify the expression in the parentheses
\[
31 - 12 + 9 = 31 - 12 + 9 = 28
\]

### Step 3: Multiply \(8 \cdot 28\)
\[
8 \cdot 28 = 224
\]

### Step 4: Substitute the values into the numerator
\[
1331 - 224 = 1107
\]

So the numerator is 1107.

### Step 5: Calculate the denominator
\[
41 \cdot 3^3 = 41 \cdot (3 \times 3 \times 3) = 41 \cdot 27 = 1107
\]

### Step 6: Final division
\[
\frac{1107}{1107} = 1
\]

Thus, the value of the given expression is:

\[
\boxed{1}
\]

Would you like further details or have any questions?

Here are some related questions:
1. What are the rules for the order of operations in expressions like this?
2. How would this problem change if we had subtraction in the denominator?
3. Could we simplify this problem using estimation techniques before calculating?
4. How does exponentiation affect the overall structure of a mathematical expression?
5. What are the applications of expressions like these in real-world contexts?

**Tip:** Always perform calculations inside parentheses first, followed by exponentiation, multiplication, and division according to the order of operations (PEMDAS/BODMAS).

Beräkna med digitalt hjälpmedel: (11^3 - 8 * (31 - 12 + 9)) / (41 * 3^3)

Learn how to calculate the expression (11^3 - 8 * (31 - 12 + 9)) / (41 * 3^3) step by step. This problem involves exponentiation and order of operations. Suitable for students in Grades 8-10.

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