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

Question

A. -4 (3+ 12^0) + 15^0 = -4 (3+1) + 1 = -4 x 4 + 1 = -15
B. -4 (3+ 12^0) + 15^0 = -4 (15) + 15 = -60 + 15 = -45
C. -4 (3+ 12^0) + 15^0 = -4 (15) + 1 = -59
D. -4 (3+ 12^0) + 15^0 = -4 (3 + 1) + 1 = -4 x 4 + 1 = -4 x 5 = -20

Answer 1

To solve the expression \(-4 (3 + 12^0) + 15^0\) using the zero power rule, we need to recognize that any non-zero number raised to the power of zero equals 1. Therefore, we have:

• \(12^0 = 1\)
• \(15^0 = 1\)

Now, we can substitute these values into the expression:

\[ -4 (3 + 12^0) + 15^0 = -4 (3 + 1) + 1 \]

Next, we perform the addition inside the parentheses:

\[ = -4 (4) + 1 \]

Now, we multiply:

\[ = -16 + 1 \]

Finally, we add:

\[ = -15 \]

Now, let's check which of the options corresponds to our calculations:

A. \(-4 (3+ 12^0) + 15^0 = -4 (3+1) + 1 = -4 \times 4 + 1 = -16 + 1 = -15\) (Correct)

B. \(-4 (3 + 12^0) + 15^0 = -4 (15) + 15 = -60 + 15 = -45\) (Incorrect)

C. \(-4 (3 + 12^0) + 15^0 = -4 (15) + 1 = -60 + 1 = -59\) (Incorrect)

D. \(-4 (3 + 12^0) + 15^0 = -4 (3 + 1) + 1 = -4 \times 4 + 1 = -16 + 1 = -15\) (This is rephrased, but still correct).

So, the correct answer is A.