Evaluate the expression.
((
–
11)2÷
–
11)2+2

Let's evaluate the expression step by step:

\[
(( -11) \cdot 2 \div (-11))^2 + 2
\]

### Step 1: Simplify the expression inside the parentheses.

The expression inside the parentheses is:

\[
(-11) \cdot 2 \div (-11)
\]

First, multiply \(-11\) by \(2\):

\[
-11 \times 2 = -22
\]

Now, divide \(-22\) by \(-11\):

\[
-22 \div (-11) = 2
\]

### Step 2: Square the result.

Now we take the result \(2\) and square it:

\[
2^2 = 4
\]

### Step 3: Add 2.

Finally, add \(2\) to the squared result:

\[
4 + 2 = 6
\]

Thus, the value of the expression is:

\[
\boxed{6}
\]

Would you like more details or have any questions?

Here are some related questions to practice:

1. Simplify \((-5) \times 3 \div (-5)\).
2. Evaluate \(((-8) \cdot 4 \div (-8))^2 + 3\).
3. Solve for \(x\) in the equation \((x \cdot 2 \div x)^2 + 5 = 9\).
4. Simplify the expression \( (-7) \times 3 \div (-7) + 5\).
5. What is the square of \(3 \div (-1)\)?

**Tip:** Always simplify the parentheses first before squaring or performing other operations.

Evaluate the expression ((-11)2 ÷ -11)² + 2

Learn how to evaluate the expression ((-11)2 ÷ -11)² + 2 with a detailed step-by-step solution. This problem involves simplifying expressions with negative numbers, exponents, and following the order of operations. Ideal for students in Grades 6-8.

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