Let S be a Noetherian separated scheme of finite Krull dimension, and (...)(S) be the motivic stable homotopy category of Morel-Voevodsky. In order to get a motivic analogue of the Postnikov tower, Voevodsky [ 25 ] constructs the slice filtration by filtering (...)(S) with respect to the smash powers of the multiplicative group (...). We show that the slice filtration is compatible with the smash product in Jardine's category Spt(...) of motivic symmetric T -spectra [ 14 ], and describe several interesting consequences that follow from this compatibility. Among them, we have that over a perfect field all the slices s_q are in a canonical way modules in Spt(...) over the motivic Eilenberg-MacLane spectrum H(...) , and if the field has characteristic zero it follows that the slices s_q are big motives in the sense of Voevodsky, this relies on the work of Levine [ 16 ], Röndings-Østvaer [ 22 ] and Voevodsky [ 26 ]. It also follows that the smash product in Spt(...) induces pairings in the motivic Atiyah-Hirzebruch spectral sequence.