+2440 Im not sure what you mean by "above," but this is my interpretation of that. I apologize if this is incorrect:
\(4^{{3+4}^5}={4^{7^5}}={4^{16807}}\approx{6.64162344 × 10^{10118}}\)
+2440 Guest, I understand your reasoning. I tend to think of equations like this when I see elementary posts:
\(\hspace {.1em} \lim_{\Delta t \to 0^+} \int_{\Delta t}^{T} \int_{\Omega}D(t_1,x) \frac{\phi(t_1-\Delta t,x)-\phi(t_1,x)}{(-\Delta t)} dx \,dt_1 \\ \hspace {3em} =\lim_{\Delta t \to 0^+} \int_{0}^{T} \! \int_{\Omega} D(t_1,x) \frac{\phi(t_1-\Delta t,x)-\phi(t_1,x)}{(-\Delta t)} \chi_{(\Delta t,T)}(t_1) dx \, dt_1 \\ \hspace {3em} = \int_{0}^{T} \! \int_{\Omega} D(t_1,x) \frac{\partial\phi}{\partial t_1}(t_1,x) dx \; dt_1 \\ \)
This is the simplified version and it easily conveys the point in basic terms.
BTW, you mangled your mathematical presentation (Buggered it up, in case you don’t know what that means).
4 above 3 plus 4 above 5 is this:
\(3^{(4 + 5^4)} \\ = 3^{(4 + 625)} \\ = 3^{(629)}\\ = 1.28608... \times 10^{300}\)
We don’t want to send students down the wrong path.
4 above 3 + 4 above 5
