What is the result of $2^{{2}^{{2}^{{2}^{0}}}}$?
It seems simple but I don't understand it.
Edit: Whoever is down-voting, please leave a comment as to why...
What is the result of $2^{{2}^{{2}^{{2}^{0}}}}$?
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$\begingroup$
algebra-precalculus
exponentiation
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3Related: [What is the order when doing $x^{y^z}$ and why?](http://math.stackexchange.com/questions/1633790/what-is-the-order-when-doing-xyz-and-why). – 2017-01-15
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2Possible duplicate of [What is the order when doing $x^{y^z}$ and why?](http://math.stackexchange.com/questions/1633790/what-is-the-order-when-doing-xyz-and-why) – 2017-02-16
3 Answers
9
$$2^0=1$$ $$2^{2^0}=2^1=2$$ $$2^{2^{2^0}}=2^2=4$$ $$2^{2^{2^{2^0}}}=2^4=16$$
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$2^{2^{2^{2^0}}}$ = $2^{2^{2^{1}}}$ = $2^{2^{2}}$ = $2^{4}$ = 16
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$2^{2^{2^{2^0}}} =2^4 =16$. Just gave the answer.