Answer
$$(13^{\sqrt2})^{\sqrt2/2}=13$$
Work Step by Step
$$(13^{\sqrt2})^{\sqrt2/2}$$
As $13\gt0$, we can apply the law of exponents here.
Applying this law: $$(a^x)^y=a^{xy}$$ we have
$$(13^{\sqrt2})^{\sqrt2/2}=13^{[\sqrt2\times\frac{\sqrt2}{2}]}=13^{2/2}=13^1=13$$
