Answer
$3x^{}b\sqrt[3]{x^2}$
Work Step by Step
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{3x^4b}\sqrt[3]{9xb^2}
\\\\=
\sqrt[3]{3x^4b(9xb^2)}
\\\\=
\sqrt[3]{27x^{4+1}b^{1+2}}
\\\\=
\sqrt[3]{27x^{5}b^{3}}
.\end{array}
Extracting the factors that are perfect powers of the index, the given expression simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{27x^{5}b^{3}}
\\\\=
\sqrt[3]{27x^{3}b^{3}\cdot x^2}
\\\\=
\sqrt[3]{(3x^{}b)^{3}\cdot x^2}
\\\\=
3x^{}b\sqrt[3]{x^2}
.\end{array}
