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The gargoogolplex is a googolplex squared, or $$(10^{10^{100}})^2 = 10^{2\cdot10^{100}}.$$[1][2] 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 (which has been named gargoogol-plexed).