Simplest form

Step 1: Rewrite $\sqrt{16x^{6}}$ as $\sqrt{(4x^{3})^{2}}$

Step 2: The power 2 cancels out our square root, so we're left with $(4x^{3})$

Step 3: Rewrite $(4x^{3})$ as $4x^{3}$

Which leaves us with $4x^{3}$

$\sqrt{16x^6} = \sqrt{(4x^3)^2} = \boxed{4x^3}$

$\sqrt{16x^{6}}=\sqrt{16}\cdot \sqrt{x^6} =4|x^3|$ As $x>0$ , we have: $\sqrt{16x^6}=4|x^3|=4x^3$