ausstellen
to exhibit
To publicly display objects, especially works of art or goods.
Das Museum stellt derzeit Werke von jungen Künstlerinnen aus.
The museum is currently exhibiting works by young female artists.

to exhibit / issue / turn off
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to exhibit
To publicly display objects, especially works of art or goods.
Das Museum stellt derzeit Werke von jungen Künstlerinnen aus.
The museum is currently exhibiting works by young female artists.

'Ausstellen' is a separable verb. The prefix 'aus-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Die Künstlerin stellt ihre neuen Bilder aus.
The artist is exhibiting her new paintings.
You can recognize the meaning of 'ausstellen' from the object. If it's about art or goods, it means 'zeigen' (to show/display). With documents, it means 'anfertigen' (to prepare/issue). With devices, it means 'ausschalten' (to switch off).
Die Galerie stellt moderne Kunst aus.
The gallery is exhibiting modern art.
In the context of 'zeigen' (to show/display), 'ausstellen' is often combined with places such as 'in einer Galerie' (in a gallery), 'im Museum' (in the museum), or 'im Schaufenster' (in the shop window). Typical objects are works of art, photos, or products.
Das Technikmuseum stellt historische Computer aus.
The technology museum is exhibiting historic computers.
When it comes to preparing documents, typical combinations are: 'ein Rezept ausstellen' (to issue a prescription), 'eine Rechnung ausstellen' (to issue an invoice), 'ein Zeugnis ausstellen' (to issue a certificate/report), or 'ein Visum ausstellen' (to issue a visa).
Die Firma muss die Rechnung innerhalb von 14 Tagen ausstellen.
The company must issue the invoice within 14 days.
In the meaning of 'ausschalten' (to switch off), 'ausstellen' is used mainly for engines, machines, or technical devices.
Der Fahrer stellte den Motor an der Ampel aus.
The driver turned off the engine at the traffic light.
to show
'zeigen' and 'ausstellen' both have to do with making something visible to others. 'zeigen' is very general: you can show someone a photo, a route, or a new phone. 'ausstellen' is used when objects are presented publicly, for example works of art in a museum or goods at a trade fair. So 'ausstellen' is more appropriate for an organized presentation for many people, while 'zeigen' also sounds natural in small everyday situations.

Im Stadtmuseum stellen junge Künstler ihre Bilder aus.
Young artists are exhibiting their paintings in the city museum.
Kannst du mir bitte den Weg zur Bibliothek zeigen?
Could you please show me the way to the library?