Question

Consider the two expressions (A and B):

A: -x to the power of 2
B:(-x) to the power of 2
Evaluate each expression for x = 2. Compare and contrast your solutions for expressions A and B. Explain in the form of a paragraph the process necessary to evaluate each expression. Describe the effect the placement of the parentheses has on the final solution.

Answer 1

The expression A results in -4, as the negative sign is applied after the squaring of 2, while expression B gives 4, because the negative sign is included in the squaring due to parentheses. This illustrates how parentheses can dramatically alter the results when involving exponents and negative numbers.

Step-by-step explanation:

The expressions A: -x to the power of 2 and B: (-x) to the power of 2 represent different calculations due to the placement of parentheses, which affects the exponentiation of negative numbers. When we evaluate expression A for x = 2, we are squaring the number first and then applying the negative sign, so A becomes -22 = -(2 × 2) = -4. In contrast, expression B includes the negative sign within the parentheses, which means the negative is also squared alongside the number. Therefore, B: (-2)2 = (-2) × (-2) = 4. The parentheses in expression B ensures that both the negative sign and the number are subject to the squaring, resulting in a positive number, while expression A applies the negative sign after the squaring, yielding a negative result. The position of parentheses is crucial in determining the outcome when dealing with exponents and negative numbers.