They sounds similar and both have exes, but extant means "still here," and extent refers to "the range of something." People get them mixed up to a certain extent.

Extant is something that's still around — you're surprised it's not extinct. It's more than just existing but also surviving when others have not. Here are some extant examples (yes, they're still here):

The roots, stumps, trunks, and foliage found in bogs are recognized as belonging to still extant species. (George P. Marsh)

He wrote in Latin an incorrect history of England, which is still extant. (Thomas Cantrell Dugdale)

Extent (with an e) means the range of something. Extent can also refer to a degree of something, such as goal achievement. Extent is also the space something covers or takes up. You might see the phrase to a lesser extent (not as much), or greater extent (more). Two is the extent of the examples below:

One's tongue slips in a longer speech to such an extent that the last word of the intended speech is said too soon. (Sigmund Freud)

He says he even sympathizes, at least to some extent, with the Occupy Wall Street protesters. (New York Times)

A helpful hint: something extant is still in existence, but the extent of something is just the range or limit, like the size, or extent, of your tent.