To analyze the expression \( 7(-5.3)^0 + 4 \cdot 9 \) and apply the Zero Power Rule, we know that any non-zero number raised to the power of 0 equals 1. Therefore, \( (-5.3)^0 = 1 \).
Substituting this back into the expression, we have:
\[ 7 \cdot (-5.3)^0 + 4 \cdot 9 = 7 \cdot 1 + 4 \cdot 9 = 7 + 36 = 43 \]
Now, let’s evaluate the provided options based on our simplification:
- 75.30 + 36: This simplifies to \( 75.3 + 36 \), which does not equal our result of 43.
- Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36: This suggests \( \frac{7}{(-5.3)^0} + 36 \), which translates to \( 7 + 36 \), not equal to 43.
- 70 + 4⋅9: This is equal to \( 70 + 36 \) which equals 106.
- Start Fraction 7 over 0 End Fraction plus 4 times 9: This is undefined as division by zero is not valid.
- Start Fraction 7 over 1 End Fraction plus 4 times 9: This suggests \( 7 + 36 \), which is equal to 43.
- 75.3 + 4⋅9: This simplifies to \( 75.3 + 36 \), which does not equal our result of 43.
The equivalent expression to \( 7(-5.3)^0 + 4 \cdot 9 \) when applying the Zero Power Rule is:
Start Fraction 7 over 1 End Fraction plus 4 times 9 (which equals \( 7 + 36 \)).