Bounding exponentiation functions with floor and ceiling functions as exponents.

Question

Suppose $x \in \mathbb{R}$ and $y,z \in \mathbb{N_{>0}}$, how can one upper bound an exponentiation function $f : \mathbb{R} \times \mathbb{N_{>0}} \times \mathbb{N_{>0}} \to \mathbb{R}$ where $$f(x,y,z) = x^{\lfloor\frac{y}{z} \rfloor}$$ we know that $\lfloor x \rfloor \leq x$ however, such a relation does not yield: $$x^{\lfloor\frac{y}{z} \rfloor} \leq x^{\frac{y}{z}}$$ since the relation does not hold for $x \in (0,1)$. Can such a function be upper bounded by removing the floor function?