I have a term of the form $(x^k -1)^s$ and I would like to find a nice looking lower bound for it without any additive terms inside of the parentheses. The reason to that is because I want something which is nice to exponentiate later.
How could I go about this? I need to find an inequality of the form:
$(x^k -1)^s \geq \hat{x}^{ks}$. And we know the following about the parameters.
$x \geq 2$
$0 \leq k \leq 1$
$s$ strictly positive