The zero power rule states that any non-zero number raised to the power of zero equals one. Therefore, we can simplify the expression given:
- \((-33)^0 = 1\) (since \(-33\) is non-zero)
- \(27^0 = 1\) (since 27 is also non-zero)
Now we can substitute these values into the expression:
\[ (-33)^0 + \frac{3}{2} (8 - 27^0) = 1 + \frac{3}{2} (8 - 1) \]
Next, simplify inside the parentheses:
\[ 8 - 1 = 7 \]
Now substitute that back into the expression:
\[ 1 + \frac{3}{2} \times 7 = 1 + \frac{21}{2} \]
Now, we need to combine the terms:
To add 1 to \(\frac{21}{2}\), we can express 1 as \(\frac{2}{2}\):
\[ 1 = \frac{2}{2} \]
So now we can add:
\[ \frac{2}{2} + \frac{21}{2} = \frac{2 + 21}{2} = \frac{23}{2} \]
Thus, the equivalent expression is:
\[ \frac{23}{2} \]
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