Final answer:
The valve responsible for admitting and exhausting steam in a steam engine is called a slide valve.
Step-by-step explanation:
The valve that admits steam to, and permits the exhaust of steam from a steam engine, is known as a slide valve. The slide valve plays a critical role in the operation of a steam engine by managing the entry and exit of steam, which in turn drives the pistons and enables the engine to do work. This function is crucial as it pertains to the efficiency and control of the steam engine, which has been a pivotal invention in transport and industry, marking significant progress since the advent of the design credited to James Watt.