To simplify the expression \(7(-5.3)^0 + 4 \cdot 9\) using the Zero Power Rule, we apply the fact that any non-zero number raised to the power of \(0\) equals \(1\). Therefore, we can simplify \((-5.3)^0\) as follows:
\[ (-5.3)^0 = 1 \]
Now substituting this back into the expression gives:
\[ 7(1) + 4 \cdot 9 \]
This simplifies to:
\[ 7 + 4 \cdot 9 \]
Next, we calculate \(4 \cdot 9\):
\[ 4 \cdot 9 = 36 \]
Now we combine the results:
\[ 7 + 36 = 43 \]
Thus, the expression simplifies to \(43\).
Among the provided options, the one that closely represents this simplification, without directly calculating the numerical result but showing the step with \(0\) exponent, is:
75.3+4⋅9 (interpreting the \( −5.3)^0\) correctly). However, since we want its numeric equivalency under operations, we'd confirm that both would yield the same resulting outcomes through respective algebraic manipulation. Thus an answer correctly aligned would remain \( 7(1)+4\cdot9\), which we calculated to \( 43\), derived from the operating principle of Zero Power Rule previously elaborated upon.
If you need any further clarification or have other expressions to evaluate, do let me know!