Irrational to power of itself is natural I've been thinking about a natural number like n so that x^x=n for some irrational x but i couldn't find anything. As i didn't know how to approach the problem at all, i tried to make some simpler cases first (n is a natural number): 1.sqrt(a)^(sqrt(a))=n for irrational sqrt(a) My approachsqrt(a)^(sqrt(a))=n=>sqrt(a)^a =n^(sqrt(a)). And here, We suppose a is even. This means the LHS would be a natural number, and thus n^(sqrt a) is natural too. This means sqrt(a)=log_n b which i think can not be true when b is not a power of n because that time i think the logarithm would be transcendental (i'm not sure). But this only disproves the case for a being even! Still if we can prove theres no such n and a, we should check the next case. 2. a^a=n for algeb

$\frac{20b}{{\left(4b^3\right)}^3}$

Which operation could we perform in order to find the number of milliseconds in a year??
${\displaystyle 60\cdot 60\cdot 24\cdot 7\cdot 365}$
${\displaystyle 1000\cdot 60\cdot 60\cdot 24\cdot 365}$
${\displaystyle 24\cdot 60\cdot 100\cdot 7\cdot 52}$
${\displaystyle 1000\cdot 60\cdot 24\cdot 7\cdot 52?}$

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A) No
B) 0
C) Yes
D) 6

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149600000000 is equal to
A)$1.496\times <!--\; \times \; -->{10}^{11}$
B)$1.496\times <!--\; \times \; -->{10}^{10}$
C)$1.496\times <!--\; \times \; -->{10}^{12}$
D)$1.496\times <!--\; \times \; -->{10}^8$

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