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1+, 20 bytes, outputs \$2^{2^8}\$
11+"*"*"*"*"*"*"*"*:
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The fastest way to get big numbers in 1+ (of which I am its creator) is to repeatedly square. One less repetition of "* will give an 18-byte representation of \$2^{2^7}\$, which however can be naively represented in 16 bytes; ...