To simplify the expression \( 5 \frac{1}{2} / \sqrt[3]{125} \):
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First, convert the mixed number \( 5 \frac{1}{2} \) to an improper fraction: \[ 5 \frac{1}{2} = \frac{11}{2} \]
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Next, simplify \( \sqrt[3]{125} \): \[ 125 = 5^3 \quad \Rightarrow \quad \sqrt[3]{125} = \sqrt[3]{5^3} = 5 \]
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Now substitute back into the expression: \[ \frac{11}{2} / 5 \]
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Dividing by \( 5 \) is the same as multiplying by its reciprocal: \[ \frac{11}{2} \times \frac{1}{5} = \frac{11}{10} \]
Therefore, the simplified expression for \( 5 \frac{1}{2} / \sqrt[3]{125} \) is: \[ \frac{11}{10} \]
Thus, the equivalent expression is \( \frac{11}{10} \).