To apply the Zero Power Rule to the expression \( 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) \), we must remember that any non-zero base raised to the power of zero equals 1. This means:
- \( (-33)^0 = 1 \)
- \( 27^0 = 1 \)
Now, we can substitute these values back into the expression:
- \( 9 \cdot (-33)^0 = 9 \cdot 1 = 9 \)
- \( 27^0 = 1 \), so \( 8 - 27^0 = 8 - 1 = 7 \)
- Thus, \( \frac{3}{2}(8 - 27^0) = \frac{3}{2} \cdot 7 = \frac{21}{2} \)
Now, we can rewrite the entire expression:
\[ 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) = 9 + \frac{21}{2} \]
To add these two values together, we can convert 9 to a fraction:
\[ 9 = \frac{18}{2} \]
Now we have:
\[ \frac{18}{2} + \frac{21}{2} = \frac{39}{2} \]
Thus, the equivalent expression is:
\[ \frac{39}{2} \]
So,
\[ 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) = \frac{39}{2} \]