The gargoogolplex is a googolplex squared, or \((10^{10^{100}})^2 = 10^{2\cdot10^{100}}.\) It was invented by Kieran Cockburn (Alistair's son), when he said "My space commander rules a gargoogolplex stars. It is a googolplex googolplexes." This number is less than \(10^{10^{101}}\). While gargoogolplex = \((10^{10^{100}})^{2}\), \(10^{10^{101}}\) = \((10^{10^{100}})^{10}\). Gargoogolplex should be interpreted as gar-googolplex, not gargoogol-plex. The latter equals to \(10^{10^{200}}\), which is a lot larger than a gargoogolplex.
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