# How do you simplify sqrt(16x^7)/sqrt(4x^4)?

$\frac{\sqrt{16 {x}^{7}}}{\sqrt{4 {x}^{4}}} = 2 x \sqrt{x}$
$\sqrt{16 {x}^{7}} = \sqrt{{\left(4 {x}^{3}\right)}^{2} \cdot x} = 4 {x}^{3} \sqrt{x}$
$\sqrt{4 {x}^{4}} = \sqrt{{\left(2 {x}^{2}\right)}^{2}} = 2 {x}^{2}$
$\frac{\sqrt{16 {x}^{7}}}{\sqrt{4 {x}^{4}}} = \frac{4 {x}^{3} \sqrt{x}}{2 {x}^{2}} = 2 x \sqrt{x}$