Solution: Step 1: Calculate the inner expression by adding the opposite of -2 to -2. The opposite of -2 is 2, so we have left(-2 + left(-(-2)right)right)2. Step 2: Simplify the expression inside the parentheses by combining -2 and 2. This results in 02. Step 3: Any number raised to the power of 2 is the number multiplied by itself. Since 0 multiplied by any number is 0, 02 equals 0. Knowledge Notes: 1. Subtraction as Adding the Opposite: The operation -2 - (-2) can be thought of as -2 + 2 because subtracting a negative is the same as adding the positive equivalent. 2. Exponents: An exponent indicates how many times to use the number in a multiplication. In this case, 02 means 0 multiplied by itself once. 3. Zero Property of Multiplication: Any number multiplied by 0 equals 0. This is why raising 0 to any positive power will always result in 0. 4. Order of Operations: When solving mathematical expressions, the order of operations must be followed. This is commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In this problem, we first resolve what's inside the parentheses, then apply the exponent. 5. Squares of Numbers: The square of any number, positive or negative, is always non-negative. This is because a number multiplied by itself yields a positive result, except for 0, which squared is still 0.

Evaluate (-2-(-2))^2

Your problem involves evaluating an algebraic expression. Specifically, the task is to calculate the square of the result obtained after subtracting a negative number (in this case, -2) from another negative number (-2). The operation inside the parentheses needs to be carried out first, following the order of operations (PEMDAS/BODMAS), which dictates that subtraction and addition occur after any necessary parentheses have been dealt with. After simplifying the expression inside the parentheses, the final step is to square the result. This problem tests basic algebraic manipulation skills and understanding of negative numbers.

$\left(\left(\right. - 2 - \left(\right. - 2 \left.\right) \left.\right)\right)^{2}$

Answer

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Solution:

Step 1:

Calculate the inner expression by adding the opposite of $-2$ to $-2$. The opposite of $-2$ is $2$, so we have $\left(-2 + \left(-(-2)\right)\right)^2$.

Step 2:

Simplify the expression inside the parentheses by combining $-2$ and $2$. This results in $0^2$.

Step 3:

Any number raised to the power of 2 is the number multiplied by itself. Since $0$ multiplied by any number is $0$, $0^2$ equals $0$.

Knowledge Notes:

Subtraction as Adding the Opposite: The operation $-2 - (-2)$ can be thought of as $-2 + 2$ because subtracting a negative is the same as adding the positive equivalent.
Exponents: An exponent indicates how many times to use the number in a multiplication. In this case, $0^2$ means $0$ multiplied by itself once.
Zero Property of Multiplication: Any number multiplied by $0$ equals $0$. This is why raising $0$ to any positive power will always result in $0$.
Order of Operations: When solving mathematical expressions, the order of operations must be followed. This is commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In this problem, we first resolve what's inside the parentheses, then apply the exponent.
Squares of Numbers: The square of any number, positive or negative, is always non-negative. This is because a number multiplied by itself yields a positive result, except for $0$, which squared is still $0$.