zero raised to infinity

Question

I encountered a question where the only condition stated that $t>0$ and was then asked to compare these two quantities

1. $0^t$
2. $t^0$

The scope of $t$ is $(0,\infty)$ and hence for infinity 1.) and 2.) are not defined . However the answer states that 2.) > 1.) as 1.) would always be zero . Is that the correct explanation?

Answer 1

$0^t=0 \lt 1 = t^0$ for all $t \in (0,\infty)$.

So the answer would be correct if it showed $t^0$ was positive.