Melody

9^(9^9) = 9^387420489 

let

$$\\y=9^{387420489} \\\\
logy=log9^{387420489}\\\\
logy=387420489log9\\\\$$

$${\mathtt{387\,420\,489}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{9}}\right) = {\mathtt{369\,693\,099.631\: \!570\: \!368\: \!587\: \!876\: \!1}}$$

$$\\logy=369693099.6315703685878761\\\\
10^{logy}=10^{369693099.6315703685878761}\\\\
y=10^{369693099}*10^{0.6315703685878761}\\\\
y=10^{0.6315703685878761}*10^{369693099}\\\\$$

$${{\mathtt{10}}}^{{\mathtt{0.631\: \!570\: \!368\: \!587\: \!876\: \!1}}} = {\mathtt{4.281\: \!247\: \!828\: \!802\: \!288\: \!2}}$$

$$9^{({9^9})}\approx 4.2812478288022882\times 10^{36969399}$$

Mmm, well I am sure your normal class teacher will be able to do it easily :)

I do not understand the placements in this question.  

The second term of a geometric sequence is 2 and the last term is 8. If the common ratio is 2√, how many geometric means are there between the first term and the last term?

This is the sequence,

$$2,\;\;2\sqrt2,\;\;4,\;\;4\sqrt2,\;\;8$$

I am not sure what geometric mean means in relation to this question.  :/

Someone should post a more conventional answer to this one but this is how I would do it

First I want to make the Bs the same.  

3:8=15:40       and      5:2=40:16

so

check

$${\mathtt{18\,030}}{\mathtt{\,\small\textbf+\,}}{\mathtt{48\,080}}{\mathtt{\,\small\textbf+\,}}{\mathtt{19\,232}} = {\mathtt{85\,342}}$$     that is great.

This probably won't be how your teacher does it but it is easy this way.  :)

@@ End of Day Wrap    Wed 12/8/15     Sydney, Australia Time   8:50pm    ♪ ♫

Hi everyone,

Our fabulous answers were contributed by CPhill, Heureka, Rubenhh, Alan, jdh3010, Dbg4thebest, luigiboi, Shaniab29544 and  Geno3141.  Thankyou   

There seems to be some disagreement here.    

Thanks Chris, of course Chris is correct :)

The derivative cannot be expressed as a function of x but it can certainly be expressed as a function of y.

Ok so why is such a bid deal made of functions verses non function ?