Alan

Looks like you are trying to use the Cosine rule to find an angle (I'll call it A) of a triangle given the lengths of the three sides.  In general, if the sides are a, b and c (with 'a' opposite angle A) then

a² = b² + c² -2*b*c*cos(A) or, rearranging this to get cos(A)

cos(A) = ( b² + c² - a²)/(2*b*c)

Here you have a = 16, b = 11, c = 12 so

$${\mathtt{cosA}} = {\frac{\left({{\mathtt{11}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{12}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{16}}}^{{\mathtt{2}}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{11}}{\mathtt{\,\times\,}}{\mathtt{12}}\right)}} \Rightarrow {\mathtt{cosA}} = {\mathtt{0.034\: \!090\: \!909\: \!090\: \!909\: \!1}}$$

and 

$${\mathtt{A}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{\left({{\mathtt{11}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{12}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{16}}}^{{\mathtt{2}}}\right)}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{11}}{\mathtt{\,\times\,}}{\mathtt{12}}\right)}}\right)} \Rightarrow {\mathtt{A}} = {\mathtt{88.046\: \!356\: \!247\: \!078^{\circ}}}$$

Just type it directly into any scientific calculator as you have written it.

If you do it without a calculator, remember that you do what's in the brackets first, then do any multiplications and divisions, then any additions and subtractions.

$${\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{20}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{20}}}{{\mathtt{10}}}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{21}} = {\mathtt{219}}$$

Since we can't have the logarithm of a negative number we must have 3/(x+8)>0, so the domain of x is all real numbers greater than -8.

Press the 2nd button then choose asin, or just type asin.

There is a subscript/superscript facility under Format.

Do you mean                                                                                                                                                          

ace₁ = 9

ace_n = ace_n-1/n² ?

If so then ace₂ = ace₁/2² or ace₂ = 9/4

ace₃ = ace₂/3² or ace₃ = (9/4)/9 or ace₃ = 1/4

ace₄ = ace₃/4² or ace₄ = (1/4)/16 or ace₄ = 1/64

 etc.

Or simply cancel the 7's:

$$-\frac{7}{8}*\frac{1}{7}=-\frac{1}{8}*\frac{1}{1}=-\frac{1}{8}=-0.125$$

0⁰ is undefined.  

There are 1000 milliWatts (mW) in one Watt (W) so multiply your number by 1000.

Press 2nd then acos, or just type acos.