a) \( 6 \sqrt[3]{9000}+7 \sqrt[3]{576} \)

To simplify the expression \( 6 \sqrt[3]{9000}+7 \sqrt[3]{576} \), let's break down each cube root separately. First, for \( 9000 \), we can write it as \( 9 \times 1000 = 9 \times 10^3 \). Thus, \( \sqrt[3]{9000} = \sqrt[3]{9} \times \sqrt[3]{1000} = \sqrt[3]{9} \times 10 \). Since \( \sqrt[3]{9} = 3^{2/3} = 3\sqrt[3]{3} \), we have: \[ 6 \sqrt[3]{9000} = 6 \times 10 \times 3^{2/3} = 60 \sqrt[3]{9} = 60 \cdot 3\sqrt[3]{3} = 180 \sqrt[3]{3}. \] Next, for \( 576 \), we can rewrite it as \( 2^6 \times 3^2 \). We find: \[ \sqrt[3]{576} = \sqrt[3]{(2^2 \cdot 3)^3} = 24. \] Putting this together: \[ 7 \sqrt[3]{576} = 7 \times 24 = 168. \] Adding both results together, we have \( 180 \sqrt[3]{3} + 168 \). In conclusion, the simplified form of the original expression is: \[ 180 \sqrt[3]{3} + 168. \]