To apply the zero power rule, we first note that any non-zero number raised to the power of zero is equal to 1. Therefore, we can simplify the expression step by step.
Starting with the expression:
\[ 9 \times (-33)^0 + \frac{3}{2} (8 - 27^0) \]
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Simplify \( (-33)^0 \): \[ (-33)^0 = 1 \] Thus, \( 9 \times (-33)^0 = 9 \times 1 = 9 \).
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Simplify \( 27^0 \): \[ 27^0 = 1 \] Therefore, inside the parentheses: \[ 8 - 27^0 = 8 - 1 = 7 \] So, \( \frac{3}{2} (8 - 27^0) = \frac{3}{2} \times 7 = \frac{21}{2} \).
Now substitute these simplified values back into the expression:
\[ 9 + \frac{21}{2} \]
To add these, we can express 9 as a fraction with a denominator of 2:
\[ 9 = \frac{18}{2} \]
Now we can add:
\[ \frac{18}{2} + \frac{21}{2} = \frac{18 + 21}{2} = \frac{39}{2} \]
Thus, the equivalent expression is:
\[ \frac{39}{2} \]
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