To simplify the expression \( \frac{\sqrt[3]{216}}{27^{1/3}} \), we can break it down using the properties of exponents and radicals.
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Compute \( 27^{1/3} \): \[ 27 = 3^3 \implies 27^{1/3} = 3^{3 \cdot \frac{1}{3}} = 3^1 = 3. \]
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Compute \( \sqrt[3]{216} \): \[ 216 = 6^3 \implies \sqrt[3]{216} = 6. \] Alternatively, \[ 216 = 2^3 \times 3^3 \implies \sqrt[3]{216} = \sqrt[3]{2^3 \cdot 3^3} = \sqrt[3]{2^3} \cdot \sqrt[3]{3^3} = 2 \cdot 3 = 6. \]
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Now rewrite the original expression: \[ \frac{\sqrt[3]{216}}{27^{1/3}} = \frac{6}{3} = 2. \]
So the answer is \( \boxed{2} \).
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