#### Answer

$2^{21}x^{52}y^6\times\sqrt{2y}$

#### Work Step by Step

$\sqrt{2^{43}x^{104}y^{13}}$
Factor out even powers.
$\sqrt{(2)(2^{42})(x^{104})(y)(y^{12})}$
Use the Product Property of Square Roots.
$\sqrt{2^{42}}\times\sqrt{2}\times\sqrt {x^{104}}\times\sqrt y\times\sqrt{y^{12}}$
Simplify square roots with variables to even powers.
$2^{21}\times\sqrt2\times x^{52}\times\sqrt y \times y^6$
Use the Product Property of Square Roots.
$2^{21}x^{52}y^6\times\sqrt{2y}$