## University Calculus: Early Transcendentals (3rd Edition)

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