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# ​4 above 3 + 4 above 5

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4 above 3 + 4 above 5

Guest May 19, 2017
#1
+2117
+1

Im not sure what you mean by "above," but this is my interpretation of that. I apologize if this is incorrect:

$$4^{{3+4}^5}={4^{7^5}}={4^{16807}}\approx{6.64162344 × 10^{10118}}$$

TheXSquaredFactor  May 19, 2017
#3
+1095
+2

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.

GingerAle  May 19, 2017
#2
+92781
+2

4 above 3 + 4 above 5

$$\frac{4}{3}+\frac{4}{5}\\ =\frac{4}{3}*\frac{5}{5}+\frac{4}{5}*\frac{3}{3}\\ =\frac{20}{15}+\frac{12}{15}\\ =\frac{32}{15}\\ =2\frac{2}{15}$$

Melody  May 19, 2017