To simplify the expression \( 12^0 \cdot 9^{-2} \cdot 5^{-2} \), we will evaluate each component step by step.
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Evaluate \( 12^0 \): According to the rules of exponents, any non-zero number raised to the power of zero is equal to 1: \[ 12^0 = 1 \]
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Evaluate \( 9^{-2} \): Negative exponents indicate the reciprocal, so: \[ 9^{-2} = \frac{1}{9^2} = \frac{1}{81} \]
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Evaluate \( 5^{-2} \): Similarly: \[ 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \]
Now, we can substitute these values back into the original expression: \[ 1 \cdot \frac{1}{81} \cdot \frac{1}{25} \]
Since multiplying by 1 does not change the value, we focus on: \[ \frac{1}{81} \cdot \frac{1}{25} = \frac{1}{81 \cdot 25} \]
Next, we calculate \( 81 \cdot 25 \): \[ 81 \cdot 25 = 2025 \]
Thus, the expression simplifies to: \[ \frac{1}{2025} \]
Therefore, the final result is: \[ \boxed{\frac{1}{2025}} \]