Question

Which of the following shows the correct process of solving −3^0+4.5
A.−3^0+4.5=−3⋅0+4.5=0+4.5=4.5
B.−3^0+4.5=−1⋅3^0+4.5=−1⋅1+4.5=−1+4.5=3.5
C.−3^0+4.5=−3+4.5=1.5
D.−3^0+4.5=(−3)^0+4.5=1+4.5=5.5

Answer 1

To find the correct process of solving \(-3^0 + 4.5\), we need to evaluate the expression step by step.

1. First, we need to recall that any number (except zero) raised to the power of \(0\) is \(1\). So, \(3^0 = 1\).

2. However, \(-3^0\) should be interpreted as \(-(3^0)\), which means \(-1\).

Now, we can evaluate the expression:
\[
-3^0 + 4.5 = -1 + 4.5 = 3.5
\]

Now let's evaluate each option:

A. \(-3^0 + 4.5 = -3\cdot0 + 4.5 = 0 + 4.5 = 4.5\)
**Incorrect** because it misinterprets the exponent.

B. \(-3^0 + 4.5 = -1 \cdot 3^0 + 4.5 = -1 \cdot 1 + 4.5 = -1 + 4.5 = 3.5\)
**Correct** because it correctly evaluates \(-3^0\) as \(-1\).

C. \(-3^0 + 4.5 = -3 + 4.5 = 1.5\)
**Incorrect** as it misrepresents \(-3^0\).

D. \(-3^0 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5\)
**Incorrect** because it wrongly treats \(-3^0\) as \((-3)^0\).

Thus, the correct answer is **B**.