\begin{aligned} \sqrt{54x^7}&=\sqrt{3^2\times 6\times \left(...

\begin{aligned} \sqrt{54x^7}&=\sqrt{3^2\times 6\times \left(x^3\right)^2\times x} \\ &=\sqrt{3^2}\times \sqrt6 \times \sqrt{\left(x^3\right)^2}\times \sqrt x \\ &=3\times \sqrt6\times x^3\times \sqrt x \\ &=3x^3\sqrt{6x} \end{aligned}