Answer
$3$
Work Step by Step
Recognize powers of 2 and 5,
$\qquad 16=2^{4}=4^{2},\quad 625=5^{4}=25^{2}$
$\sqrt[3]{{\sqrt[4]{16}}+{\sqrt[2]{625}}}=\sqrt[3]{2+25}$
$=\sqrt[3]{2+25}=\sqrt[3]{27}$
... recognize a power of 3, $\quad 27=3^{3}$
$=3$
