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Exponentiation refers to raising a number to a certain power, which means multiplying that number by itself a specified number of times. For instance, in the exercise given, we need to calculate \((-12)^2\). This means we multiply \(-12\) by itself. So, \((-12) \times (-12) = 144\). Remember, multiplying two negative numbers results in a positive product.

Exponentiation is a fundamental operation in mathematics as it allows us to express repeated multiplication succinctly. As a tip, always notice the sign of the numbers involved, especially when dealing with negatives. If the base number (the number being exponentiated) is negative and the power is even, the result is positive.

Multiplication with integers involves taking two whole numbers, which can be either positive or negative, and finding their product. In the exercise, we multiply \(-1\) with \(2\). In cases where one number is negative and the other is positive, as seen in \((-1) \times 2\), the result is always negative, giving us \(-2\).

Key points when multiplying integers include:

• Positive \(\times\) Positive = Positive
• Positive \(\times\) Negative = Negative
• Negative \(\times\) Positive = Negative
• Negative \(\times\) Negative = Positive

These rules are consistent and crucial for solving broader arithmetic problems.
Understanding these rules helps simplify complex algebraic expressions and equations more effectively.

In integer operations, addition and subtraction require careful attention to the signs of the numbers involved. In our solution, we see the task \(144 + (-2) - 6\). Here we perform the operations step by step. First, add \(144\) and \(-2\). Instead of directly adding, think of it as \(144 - 2 = 142\), because adding a negative is the same as subtracting.

Next, handle the subtraction part: \(142 - 6 = 136\). When subtracting, move to the left on the number line, which leads to a smaller number.

Tips for effective integer addition and subtraction:

• Adding a negative is the same as subtraction.
• Subtracting a negative becomes addition.

Mastering these concepts ensures accuracy in arithmetic and algebra, paving the way for tackling more advanced math challenges efficiently.