Simplify the Radical Expression x^3 square root of x^7

$x^{3} \sqrt{x^{7}}$

Rewrite $x^{7}$ as ${(x^{3})}^{2} x$ .

Factor out $x^{6}$ .

$x^{3} \sqrt{x^{6} x}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$x^{3} \sqrt{{(x^{3})}^{2} x}$

Pull terms out from under the radical.

$x^{3} (| x^{3} | \sqrt{x})$

Reorder factors in $x^{3} (| x^{3} | \sqrt{x})$ .

$x^{3} | x^{3} | \sqrt{x}$