Errata: 8:12 - Tesla did *not* promise 5 times the "energy density" (Wh/kg) nor 6 times the "power density" (W/kg), as you said. Instead, they promised 5 times the energy (absolute value per cell, in Ah) and 6 times the power (absolute value per cell, in W) per cell from the 4680 cell over the 2170 cell, which itself is a factor 5.5 in volume. So, basically at that point in time, they promised: a bigger bucket will likewise hold proportionally more energy and deliver proportionally more power. As the form factor 4680 battery packs would have about 1/5 in the number of cells over packs with form factor 2170 cells, this meant basically no progress in these regards, but only in lowering production complexity. Instead, a a true 5x improvement energy density (Wh/kg) or power density (W/kg) would be basically an enormous breakthrough with about 5 times the range (+400%) or 6 times the power (+500%) from an equally heavy battery pack. But as can be seen from the promise on "+16% range increase": this was not meant. They can achieve those +16% by simply fitting a few more cells with revised packaging and/or by slightly reducing the vehicle mass or drag.
Errata: 8:12 - Tesla did *not* promise 5 times the "energy density" (Wh/kg) nor 6 times the "power density" (W/kg), as you said. Instead, they promised 5 times the energy (absolute value per cell, in Ah) and 6 times the power (absolute value per cell, in W) per cell from the 4680 cell over the 2170 cell, which itself is a factor 5.5 in volume. So, basically at that point in time, they promised: a bigger bucket will likewise hold proportionally more energy and deliver proportionally more power. As the form factor 4680 battery packs would have about 1/5 in the number of cells over packs with form factor 2170 cells, this meant basically no progress in these regards, but only in lowering production complexity.
Instead, a a true 5x improvement energy density (Wh/kg) or power density (W/kg) would be basically an enormous breakthrough with about 5 times the range (+400%) or 6 times the power (+500%) from an equally heavy battery pack. But as can be seen from the promise on "+16% range increase": this was not meant. They can achieve those +16% by simply fitting a few more cells with revised packaging and/or by slightly reducing the vehicle mass or drag.