# Exponents are not so straightforward!

Algebra Level 5

Let $$x_0$$ be the number of positive real solutions to $\large x^{1.2^{1.2}} = 1.2^x$ And $$y_0$$ be the number of positive real solutions to $\large y^{x_0^{x_0}} =x_0^y$ Find the sum of all real positive solutions $$z$$ to the equation $\large z^{y_0}=x_0^z$

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