The reproductive hyphae that grows out of a fungus is called a conidiophore.

Here's why:

* Hyphae: These are the thread-like filaments that make up the body of a fungus.

* Conidiophore: This is a specialized hypha that bears conidia, which are asexual spores. Conidia are the primary means of reproduction for many fungi.

Other terms related to fungal reproduction:

* Sporangiophore: A specialized hypha that bears sporangia, which are enclosed structures containing spores.

* Fruiting body: A complex structure produced by some fungi that contains spores. Examples include mushrooms and puffballs.

Let me know if you have any other questions about fungi!