To express the prime factorization \( 23 \cdot 5^2 \cdot 11 \) as a whole number, we need to calculate the product step by step.
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Calculate \( 5^2 \): \[ 5^2 = 25 \]
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Now multiply \( 23 \), \( 25 \), and \( 11 \): \[ 23 \cdot 25 \cdot 11 \]
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First, multiply \( 23 \) and \( 25 \): \[ 23 \cdot 25 = 575 \]
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Now multiply \( 575 \) by \( 11 \): \[ 575 \cdot 11 = 6325 \]
So, the expression \( 23 \cdot 5^2 \cdot 11 \) as a whole number is: \[ \boxed{6325} \]