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?

Question

−4 (3 + 12^0) + 15^0 = −4 (3 + 1) + 1 = −4 ⋅ 4 + 1 = −4 ⋅ 5 = −20

−4 (3 + 12^ 0) + 15^0 = −4 (15) + 15 = −60 + 15 = −45

−4 (3 + 12^0) + 15^0 = −4 (3 + 1) + 1 = −4 ⋅ 4 + 1 = −16 + 1 = −15

−4 (3 + 12^0) + 15^0 = −4 (15) + 1 = −60 + 1 = −59

Answer 1

Let's solve the expression \(-4 (3 + 12^0) + 15^0\) step by step, correctly applying the Zero Power Rule.

1. According to the Zero Power Rule, any non-zero number raised to the power of 0 equals 1. Therefore:

   • \(12^0 = 1\)
   • \(15^0 = 1\)

2. Substituting these values into the expression: \[ -4 (3 + 1) + 1 \]

3. Now simplify inside the parentheses: \[ -4 (4) + 1 \]

4. Next, multiply \(-4\) by \(4\): \[ -16 + 1 \]

5. Finally, add \(-16\) and \(1\): \[ -15 \]

Therefore, the correct process of solving the expression is:

\(-4 (3 + 12^0) + 15^0 = -4 (3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15\)

The correct statement from the options you provided is:

−4 (3 + 12^0) + 15^0 = −4 (3 + 1) + 1 = −4 ⋅ 4 + 1 = −16 + 1 = −15.