i have a variable $c$ such that $0\leq c\leq1$ and a variable $t>0$ can i always say that $0\leq(c^t)\leq1$ ? What i found difficult is the exponentiation between for example $0<c<1$ and $0<t<1$
I tried to do some computation but i'm not sure that i'm right
If this makes you feel more comfortable: when $c=d^{-1}$ (where therefore $d>1$) then $c^t=d^{-t}=(d^t)^{-1}$. For $t>0$ this is indeed in $(0,1)$, since $d^t>1$.