Why And How are Unbranched chains of hydrocarbons easily biodegraded?
Here is a study1 showing this is the case, that generally speaking, branched hydrocarbons are more difficult to degrade, especially those exhibiting anteiso-terminal branching (branching  on the third carbon). Both the study and a book on oil spill forensics2 hypothesize that steric hindrance is the  mechanism responsible. They state, respectively:


  If alkyl branches are located near the terminus, it seems likely that decreased biodegradability could be the result of steric inhibition of terminal oxidizing enzymes





  Complex branching hinders both the initial oxidation and the subsequent lipid catabolism apparently because tertiary and quarternary carbon atoms interfere by steric hindrance with the oxidation enzymes.


However, this is not always the case as Boethling3 explains when discussing design objectives for molecule biodegradability:


  Similarly there is a commonly held view that any branching, for example, even a single methyl group on an otherwise linear alkyl group, is to be avoided. This is a gross oversimplification. All that can be said with any confidence is that quaternary carbon is usually to be avoided, as is extensive methyl chain branching, which has no strict definition.




1 Schaeffer, T. L., Cantwell, S. G., Brown, J. L., Watt, D. S., &amp; Fall, R. R. (1979). Microbial Growth on Hydrocarbons: Terminal Branching Inhibits Biodegradation. Applied and Environmental Microbiology, 38(4), 742-746. Retrieved from https://aem.asm.org/

2 Wang, Z., &amp; Stout, S. (2006). Oil Spill Environmental Forensics: Fingerprinting and Source Identification (1st ed.). Burlington, MA: Academic Press.

3 Boethling, R. S., Sommer, E., &amp; DiFiore, D. (2007). Designing Small Molecules for Biodegradability. Chemical Reviews, 107(6), 2207–2227. https://doi.org/10.1021/cr050952t