Which of the following shows the correct process of solving −3^0 + 4.5?

Question

options:

−3^0 + 4.5 = −1 ⋅ 3^0 + 4.5 = −1 ⋅ 1 + 4.5 = −1 + 4.5 = 3.5

−3^0 + 4.5 = -3 ⋅ 0 + 4.5 = 0 + 4.5 = 4.5

−3^0 + 4.5 = −3 + 4.5 = 1.5

−3^0 + 4.5 = (−3)^0 + 4.5 = 1 + 4.5 = 5.5

Answer 1

Let's evaluate the expression \(-3^0 + 4.5\) step by step.

First, it's important to note that \(3^0 = 1\), for any non-zero number. Therefore, when we compute \(-3^0\), we interpret it as \(-1 \cdot 3^0 = -1 \cdot 1 = -1\).

Now we can evaluate the expression:

\[ -3^0 + 4.5 = -1 + 4.5 = 3.5 \]

Now let's check the provided options:

1. Option 1: \(-3^0 + 4.5 = −1 ⋅ 3^0 + 4.5 = −1 ⋅ 1 + 4.5 = −1 + 4.5 = 3.5\) - This is correct.

2. Option 2: \(-3^0 + 4.5 = -3 ⋅ 0 + 4.5 = 0 + 4.5 = 4.5\) - This is incorrect because \(3^0\) is not multiplied by \(-3\).

3. Option 3: \(-3^0 + 4.5 = −3 + 4.5 = 1.5\) - This is incorrect because it misinterprets \(3^0\) as \(-3\).

4. Option 4: \(-3^0 + 4.5 = (−3)^0 + 4.5 = 1 + 4.5 = 5.5\) - This is also incorrect because \((−3)^0 = 1\) isn't the correct treatment of \(-3^0\).

The correct process is shown in Option 1. Therefore, the answer is:

−3^0 + 4.5 = −1 ⋅ 3^0 + 4.5 = −1 ⋅ 1 + 4.5 = −1 + 4.5 = 3.5.