KöMaL 2025 C1866

Three segments are given with lengths $1$, $a$ and $b$ (where $a\neq 1$ and $b\neq 1$). Describe a way to construct segments of lengths ${\frac{1}{a}}$, $a\cdot b$ and $a^2\cdot b^3$. The elementary constructions, e.g. bisecting an angle, reflecting across a line, etc. do not have to be described in detail.