To simplify the expression \( 9 \cdot (-33)^0 + \frac{3}{2} (8 - 27^0) \) using the Zero Power Rule, we need to remember that any non-zero number raised to the power of 0 is equal to 1:
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Applying the Zero Power Rule:
- \( (-33)^0 = 1 \) (since it is non-zero)
- \( 27^0 = 1 \) (since it is also non-zero)
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Substituting these values into the expression:
- \( 9 \cdot 1 + \frac{3}{2} (8 - 1) \)
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Simplifying further:
- This simplifies to \( 9 + \frac{3}{2} (8 - 1) = 9 + \frac{3}{2} \cdot 7 \)
- \( = 9 + \frac{21}{2} \)
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Finding a common denominator to add:
- Convert \( 9 \) into a fraction: \( 9 = \frac{18}{2} \)
- Now we can add: \( \frac{18}{2} + \frac{21}{2} = \frac{39}{2} \)
So the final simplified expression is:
\[ \frac{39}{2} \]
Thus, the equivalent expression is \( 9 \cdot 1 + \frac{3}{2} (8 - 1) \) or in your requested form, substituting:
\[ 9 \cdot (1) + \frac{3}{2}(8 - 1) \]
Where you can see the parts as \( ? ⋅ ? + \frac{3}{2}(? – ?) \):
- \( 9 \cdot 1 + \frac{3}{2}(8 - 1) \) corresponds to \( 9 \cdot ? + \frac{3}{2} (? - ?) = 9 \cdot 1 + \frac{3}{2}(8 - 1) \).
Thus the answer is: \[ 9 ⋅ 1 + \frac{3}{2}(8 - 1) \]
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