To simplify the expression \(\frac{\sqrt[3]{216}}{27^{\frac{1}{3}}}\), we can start by rewriting each part using exponent properties.
First, we can rewrite \( \sqrt[3]{216} \) and \( 27^{\frac{1}{3}} \):
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Calculating \(\sqrt[3]{216}\): \[ 216 = 6^3 \] Therefore, \[ \sqrt[3]{216} = \sqrt[3]{6^3} = 6. \]
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Calculating \(27^{\frac{1}{3}}\): \[ 27 = 3^3 \] Thus, \[ 27^{\frac{1}{3}} = \sqrt[3]{27} = \sqrt[3]{3^3} = 3. \]
Putting it all together: \[ \frac{\sqrt[3]{216}}{27^{\frac{1}{3}}} = \frac{6}{3} = 2. \]
Thus, the expression \(\frac{\sqrt[3]{216}}{27^{\frac{1}{3}}}\) simplifies to \(2\).
The equivalent answer is: \[ \boxed{2}. \]