How can we take the LaPlace of a function raised to the power?

Question

For example:

$\mathcal{L}$((t-1)^1)

Following simple linearity, we achieve the answer. However, following the power of theorem:

(I'm not proficient enough in LaTex to write this...) I get the wrong answer with an extra factor of $s^1 in front.

To my knowledge, the answer should simply be:

$[\frac{1}{s^2}-\frac{1}{s}]

Why does this theorem not work? (I know it will and I'm doing something silly, please correct me.)

The theorem I am trying to apply is attached:

Answer 1

It's fairly standard notation that

$$\Large{f^{(n)}}$$

refers to the $n$-th derivative of the function $x$. The $n$-th power would be represented as $f^n$, or better as $(f)^n$ to avoid confusion with the operation of composition $n$ times.