To simplify the expression \( 7(-5.3)^0 + 4 \cdot 9 \) using the Zero Power Rule, we need to remember that any non-zero number raised to the power of 0 equals 1. Therefore, we have:
\[ (-5.3)^0 = 1 \]
Now we can substitute this back into the expression:
\[ 7 \cdot 1 + 4 \cdot 9 \]
This simplifies to:
\[ 7 + 4 \cdot 9 \]
Now calculating \( 4 \cdot 9 \):
\[ 4 \cdot 9 = 36 \]
Thus, our expression is now:
\[ 7 + 36 \]
Finally, simplifying this gives:
\[ 43 \]
Now looking at the provided options, the one that matches our finding is:
\[ 7 \cdot 1 + 4 \cdot 9 \]
So the answer is:
\[ 71 + 4 \cdot 9 \]
Indicating that the correct option is indeed \( \text{71 + }4 \cdot 9 \).