b. \( 12 \sqrt[3]{2 z^{5}}-z \sqrt[3]{54 z^{2}}= \)

To simplify the expression \( 12 \sqrt[3]{2 z^{5}} - z \sqrt[3]{54 z^{2}} \), we begin by breaking down each term. The first term can be rewritten as: \[ 12 \sqrt[3]{2z^{5}} = 12 \sqrt[3]{2} \sqrt[3]{z^5} = 12 \sqrt[3]{2} z^{5/3} \] The second term is simplified as follows: \[ z \sqrt[3]{54 z^{2}} = z \sqrt[3]{54} \sqrt[3]{z^2} = z \sqrt[3]{54} z^{2/3} = \sqrt[3]{54} z^{5/3} \] Now, let's combine: \[ 12 \sqrt[3]{2} z^{5/3} - \sqrt[3]{54} z^{5/3} = (12 \sqrt[3]{2} - \sqrt[3]{54}) z^{5/3} \] So, putting it all together gives us: \[ (12 \sqrt[3]{2} - \sqrt[3]{54}) z^{5/3} \] And that's your simplified expression!