Answer
$5b\sqrt[]{b}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\sqrt[]{9b^3}-\sqrt[]{25b^3}+\sqrt[]{49b^3}
\\=
\sqrt[]{9b^2\cdot b}-\sqrt[]{25b^2\cdot b}+\sqrt[]{49b^2\cdot b}
\\=
3b\sqrt[]{b}-5b\sqrt[]{b}+7b\sqrt[]{b}
\\=
5b\sqrt[]{b}
.\end{array}