Upon further reading, it seems your third example is valid.  One must
use parentheses if the entire exponent is 2π, as in 3^(2pi), otherwise
3^2pi should evaluate to 9pi as you said.

Also from the same further reading, using your second example, if not
wanting to simply write/enter 250000000*1.01^20 we should use
(250000000)(1.01)^20.

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https://bugs.launchpad.net/bugs/1161670

Title:
  Order of operations is incorrect for exponents and parentheses

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