  We investigate pseudopowers of singular cardinals, and show that deduce some
consequences for cardinal arithmetic. For example, we show that in {\sf ZFC}
that
$$\cov(\mu,\mu,\theta,\sigma)=\cov(\mu,\mu,(\cf\mu)^+,\sigma)+\cov(\mu,\mu,\theta,\sigma^+)$$
whenever $\aleph_1\leq\sigma=\cf(\sigma)<\cf(\mu)<\theta<\mu$, and use recent
work of Gitik to show that both summands in the equation are required.
