Answer
$6x^3\sqrt[]{x}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\sqrt[]{4x^7}+9x^2\sqrt[]{x^3}-5x\sqrt[]{x^5}
\\=
\sqrt[]{4x^6\cdot x}+9x^2\sqrt[]{x^2\cdot x}-5x\sqrt[]{x^4\cdot x}
\\=
2x^3\sqrt[]{x}+9x^2\cdot x\sqrt[]{x}-5x\cdot x^2\sqrt[]{x}
\\=
2x^3\sqrt[]{x}+9x^3\sqrt[]{x}-5x^3\sqrt[]{x}
\\=
6x^3\sqrt[]{x}
.\end{array}
