To solve the expression \(-4(3 + 12^{0} + 15^{0})\) using the zero power rule, we first need to evaluate the terms inside the parentheses. The zero power rule states that any non-zero number raised to the power of zero equals one, i.e., \(x^0 = 1\) for any \(x \neq 0\).
-
Evaluate \(12^0\): \[ 12^0 = 1 \]
-
Evaluate \(15^0\): \[ 15^0 = 1 \]
Now we can substitute these values back into the expression inside the parentheses:
\[ 3 + 12^{0} + 15^{0} = 3 + 1 + 1 = 5 \]
Next, we substitute this value back into the expression:
\[ -4(3 + 12^{0} + 15^{0}) = -4(5) \]
Finally, we calculate \(-4 \times 5\):
\[ -4 \times 5 = -20 \]
Thus, the final answer is:
\[ \boxed{-20} \]