b) \( \left(6^{\frac{2}{3}} \cdot 16^{\frac{1}{6}}\right) \)

1. Express \(6^{\frac{2}{3}}\) in terms of its prime factors: \[ 6^{\frac{2}{3}} = \left(2 \cdot 3\right)^{\frac{2}{3}} = 2^{\frac{2}{3}} \cdot 3^{\frac{2}{3}}. \] 2. Express \(16^{\frac{1}{6}}\) in terms of its prime factors: \[ 16 = 2^4 \quad \Rightarrow \quad 16^{\frac{1}{6}} = \left(2^4\right)^{\frac{1}{6}} = 2^{\frac{4}{6}} = 2^{\frac{2}{3}}. \] 3. Multiply the expressions: \[ 6^{\frac{2}{3}} \cdot 16^{\frac{1}{6}} = \left(2^{\frac{2}{3}} \cdot 3^{\frac{2}{3}}\right) \cdot 2^{\frac{2}{3}} = 2^{\frac{2}{3}+\frac{2}{3}} \cdot 3^{\frac{2}{3}} = 2^{\frac{4}{3}} \cdot 3^{\frac{2}{3}}. \] 4. Combine the exponents using the property \(a^{\frac{p}{q}} \cdot b^{\frac{p}{q}} = (a \cdot b)^{\frac{p}{q}}\) if applicable: \[ 2^{\frac{4}{3}} \cdot 3^{\frac{2}{3}} = \left(2^4 \cdot 3^2\right)^{\frac{1}{3}} = \left(16 \cdot 9\right)^{\frac{1}{3}} = \left(144\right)^{\frac{1}{3}}. \] The final simplified expression is: \[ \left(6^{\frac{2}{3}} \cdot 16^{\frac{1}{6}}\right) = \left(144\right)^{\frac{1}{3}}. \]