To simplify the expression \( 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) \), we will use the zero power rule, which states that any non-zero number raised to the power of 0 equals 1.
- Start by simplifying the terms with exponent 0:
- \((-33)^0 = 1\)
- \(27^0 = 1\)
Now we can rewrite the expression:
\[ 9 \cdot 1 + \frac{3}{2}(8 - 1) \]
- Simplifying further:
- From the first term: \(9 \cdot 1 = 9\)
- For the second part, calculate \(8 - 1 = 7\).
Now substitute this back into the expression:
\[ 9 + \frac{3}{2} \cdot 7 \]
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Next, calculate \(\frac{3}{2} \cdot 7\):
- \(\frac{3}{2} \cdot 7 = \frac{21}{2}\)
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Now add \(9\) to \(\frac{21}{2}\). To do this, convert \(9\) to have a common denominator:
\[ 9 = \frac{18}{2} \]
Thus, the expression now becomes:
\[ \frac{18}{2} + \frac{21}{2} = \frac{39}{2} \]
Therefore, the equivalent expression is:
\[ \frac{39}{2} \]
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