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.