# Is it impossible to calculate any power with limited mathimatical operations?

Before I start this question, I am talking about calculating any calculatable power, with real numbers. EG: $2^{7.16}$

Consider such a problem, where you are asked to calculate a power like the one above without using logarithms

Can you calculate something like $2^{7.16}$ with only these operations mentioned above? (or approximate it), or is it simply impossible?

Note that $\sqrt[n]{x}=y\implies y^n -x = 0$ so we can use a root finding algorithm to find arbitrary $n$th roots.
With that in hand, we can observe $2^{7.16} = 2^{716/100} = \sqrt[100]{2^{716}}$.