  Over the last years some interest has been gathered by $f(Q)$ theories, which
are new candidates to replace Einstein's prescription for gravity. The
non-metricity tensor $Q$ allows to put forward the assumption of a free
torsionless connection and, consequently, new degrees of freedom in the action
are taken into account. This work focuses on a class of $f(Q)$ theories,
characterized by the presence of a general power-law term which adds up to the
standard (linear in) $Q$ term in the action, and on new cosmological scenarios
arising from them. Using the Markov chain Montecarlo method we carry out
statistical tests relying upon background data such as Type Ia Supernovae
luminosities and direct Hubble data (from cosmic clocks), along with Cosmic
Microwave Background shift and Baryon Acoustic Oscillations data. This allows
us to perform a multifaceted comparison between these new cosmologies and the
(concordance) $\Lambda$CDM setup. We conclude that, at the current precision
level, the best fits of our $f(Q)$ models correspond to values of their
specific parameters which make them hardly distinguishable from our General
Relativity "\'echantillon", that is $\Lambda$CDM.
