The zero power rule states that any non-zero number raised to the power of zero is equal to 1. This is applicable in the given expression as follows:
- For \((-33)^0\), according to the zero power rule, this equals 1.
- For \(27^0\), this also equals 1.
Now, let's simplify the expression step by step:
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Start with the original expression: \[ 9 \times (-33)^0 + \frac{3}{2} (8 - 27^0) \]
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Apply the zero power rule: \[ 9 \times 1 + \frac{3}{2} (8 - 1) \]
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This simplifies to: \[ 9 + \frac{3}{2} (7) \]
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Now, calculate \(\frac{3}{2} \times 7\): \[ \frac{3 \times 7}{2} = \frac{21}{2} \]
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Now add \(9\) (which can be written as \(\frac{18}{2}\) to have a common denominator): \[ \frac{18}{2} + \frac{21}{2} = \frac{39}{2} \]
So, the equivalent expression is: \[ \frac{39}{2} \]