The Zero Power Rule states that any non-zero number raised to the power of zero equals one. Therefore, in the expression \(9 \cdot (-33)^0\), we can simplify \((-33)^0\) as follows:
\[ (-33)^0 = 1 \]
So,
\[ 9 \cdot (-33)^0 = 9 \cdot 1 = 9 \]
Next, we simplify the second part of the expression:
\[ 32(8 - 27^0) \]
Again applying the Zero Power Rule, we find:
\[ 27^0 = 1 \]
Thus,
\[ 8 - 27^0 = 8 - 1 = 7 \]
Now we can combine everything into the simplified expression:
\[ 9 + \frac{3}{2} \cdot 7 \]
Now we can calculate \(\frac{3}{2} \cdot 7\):
\[ \frac{3}{2} \cdot 7 = \frac{21}{2} \]
Putting all components together, we have:
\[ 9 + \frac{21}{2} \]
Now convert 9 into a fraction for easy addition:
\[ 9 = \frac{18}{2} \]
Thus, adding:
\[ \frac{18}{2} + \frac{21}{2} = \frac{39}{2} \]
So the final equivalent expression becomes:
\[ \frac{39}{2} \]
To summarize, the simplified equivalent expression to \(9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0)\) is:
\[ 9 + \frac{3}{2}(7) \]
Which numerically computes to:
\[ \frac{39}{2} \]
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