In this paper, we provide several characterizations of a spherically quasinormal tuple \(\textbf{T}\) in terms of its normal extension, as well as in terms of powers of the associated elementary operator \(\Theta _{\textbf{T}}(I)\) . Utilizing these results, we establish that the powers of spherically quasinormal tuples remain spherically quasinormal. Additionally, we prove that the subnormal n-th roots of spherically quasinormal tuples must also be spherically quasinormal, thereby resolving a multivariable version of a previously posed problem by Curto et al. in [17]. Furthermore, we investigate the connection between a (pure) spherically quasinormal tuple \(\textbf{T}\) , its minimal normal extension \(\textbf{N}\) , and its dual \(\textbf{S}\) . Among other things, we show that \(\textbf{T}\) inherits the spherical polar decomposition from \(\textbf{N}\) . Finally, we also demonstrate that \(\textbf{N}\) is Taylor invertible if and only if \(\textbf{T}\) and \(\textbf{S}\) have closed ranges.
