Question

Which of the following shows the correct process of solving -4(3 + 12^0) + 15^0 by generating an equivalent expression using the zero power rule?

Answer 1

To solve the expression \(-4(3 + 12^0) + 15^0\), we can use the zero power rule, which states that any non-zero number raised to the power of 0 is equal to 1.

Let's break it down step-by-step:

1. **Identify the zero powers:**
- \(12^0 = 1\)
- \(15^0 = 1\)

2. **Substitute the values into the expression:**
\[
-4(3 + 12^0) + 15^0 = -4(3 + 1) + 1
\]

3. **Simplify the expression inside the parentheses:**
\[
3 + 1 = 4
\]
So, the expression now looks like:
\[
-4 \cdot 4 + 1
\]

4. **Multiply:**
\[
-4 \cdot 4 = -16
\]
Therefore, the expression simplifies to:
\[
-16 + 1
\]

5. **Add the final terms:**
\[
-16 + 1 = -15
\]

So the final result of solving \(-4(3 + 12^0) + 15^0\) is \(-15\). The correct process involved recognizing and applying the zero power rule to simplify the expression step-by-step.