To apply the Zero Power Rule, we first need to recognize that any non-zero number raised to the power of 0 equals 1. Thus, we can simplify the expression given in the problem:
-
Starting Expression:
\( 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) \) -
Applying the Zero Power Rule:
- \( (-33)^0 = 1 \)
- \( 27^0 = 1 \)
Now we substitute these values into the expression:
\[ 9 \cdot 1 + \frac{3}{2}(8 - 1) \]
- Simplifying Further:
- The first term simplifies to \( 9 \).
- The second term becomes \( \frac{3}{2}(7) \) since \( 8 - 1 = 7 \).
Calculating \( \frac{3}{2} \cdot 7 \):
\[ \frac{3 \times 7}{2} = \frac{21}{2} \]
- Final Simplified Expression:
Thus, the entire expression simplifies to:
\[ 9 + \frac{21}{2} \]
To express this as a single fraction, we can convert \( 9 \) into a fraction with a denominator of \( 2 \):
\[ 9 = \frac{18}{2} \]
So now we can add:
\[ \frac{18}{2} + \frac{21}{2} = \frac{39}{2} \]
- Conclusion:
So the equivalent expression for \( 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) \) is:
\[ \frac{39}{2} \]
Thus, the answer is:
\[ \frac{39}{2} \]