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Exponential notation is a way of expressing repeated multiplication of the same number. In the exercise, we encounter the term \( (-1)^2 \) which demonstrates the concept of exponentiation. Here the number -1 is being multiplied by itself precisely because the exponent is 2. The general formula for an exponential term is \( a^n \), where \( a \) is the base and \( n \) is the exponent, indicating how many times the base is to be used in a multiplication.

In our example, applying exponentiation simplifies \( (-1)^2 \) to 1. The negative sign in the base floats away as any negative number raised to an even exponent will result in a positive outcome due to the nature of multiplication involving even numbers of negative terms—negative times negative always gives a positive. Consequently, \( (-1) * (-1) = 1 \), which is an important note when calculating such expressions.

Basics of Multiplication

Multiplication is the operation that combines groups of equal sizes. It's one of the four fundamental operations in arithmetic and can be considered a shortcut for repeated addition. In our exercise, after we've applied exponentiation, we multiply the resulting 1 by 3, as indicated by \( 1*3 \), which equates to the addition of one, three times. Similarly, multiplying -3 by 2 as in \( -3*2 \) is equivalent to adding -3 twice.

Hence, these multiplication operations are essential to simplify expressions before we address any addition or subtraction that follows. Moreover, it's crucial to observe the order of operations, generally denoted as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), which states that multiplication should be performed before addition in most circumstances.

Addition brings separate quantities together to find their total. In algebraic operations like the one in our example, addition often comes after exponentiation and multiplication have been completed. At this stage, the expression in our example has been reduced to \( 3 + (-6) \), at which point we simply combine the numbers.

Here's a key tip: adding a negative number is the same as subtracting its absolute value. Thus, when we add 3 and -6, we are effectively subtracting 6 from 3, leading to a result of -3. It's beneficial to understand the concept of 'absolute value', which is the distance of a number from zero, disregarding its sign. Therefore, when faced with such an operation, one should think of pulling numbers along a number line, where adding a negative number means moving left (towards lesser values) as opposed to moving right (towards greater values) when adding positive numbers.