[0.05(-$34 – $4.1)2 + 0.20(-$22 – $4.1)2 + 0.50($12 – $4.1)2 + 0.20($14 – $4.1)2 + 0.05($28 – $4.1)2]½

Because of the positioning of the 2's and the 1/2 on the outside, it looks to me as if the following is what is wanted:

$${\left[{\mathtt{0.05}}{\mathtt{\,\times\,}}{\left({\mathtt{\,-\,}}{\mathtt{34}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.2}}{\mathtt{\,\times\,}}{\left({\mathtt{\,-\,}}{\mathtt{22}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.5}}{\mathtt{\,\times\,}}{\left({\mathtt{12}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.2}}{\mathtt{\,\times\,}}{\left({\mathtt{14}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.05}}{\mathtt{\,\times\,}}{\left({\mathtt{28}}{\mathtt{\,-\,}}{\mathtt{4.1}}\right)}^{{\mathtt{2}}}\right]}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)} = {\mathtt{16.976\: \!159\: \!754\: \!196\: \!471\: \!4}}$$

or, ≈ $16.98

(I copied and pasted rather than rewriting this, then inserted ^ and * as appropriate and changed the long horizontal lines to - signs.)

[0.05(-$34 – $4.1)2 + 0.20(-$22 – $4.1)2 + 0.50($12 – $4.1)2 + 0.20($14 – $4.1)2 + 0.05($28 – $4.1)2]½

=[0.05(-38.10)2 + 0.20(-26.10)2 + 0.50(7.90)2 + 0.20(9.90)2 + 0.05(23.90)2]*0.5

=0.05*-38.10 + 0.20*-26.10 + 0.50*7.90 + 0.20*9.90 + 0.05*23.90

=0.05(-38.10+7.9+23.9)+0.20(-26.10+9.9)

=0.05(-38.10+31.8)+0.20(-16.2)

=0.05(-8.10+1+0.8)+-3.24

=0.05(-7.10+0.8)-3.24

=0.05(-6.3)-3.24

=-0.315-3.24

= -3.555     I suppose i have made an error but I cannot find it.   

$$\left({\mathtt{0.05}}{\mathtt{\,\times\,}}{\mathtt{\,-\,}}\left({\mathtt{38.1}}{\mathtt{\,\times\,}}{\mathtt{2}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{0.2}}{\mathtt{\,\times\,}}{\mathtt{\,-\,}}\left({\mathtt{26.1}}{\mathtt{\,\times\,}}{\mathtt{2}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{7.9}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.2}}{\mathtt{\,\times\,}}{\mathtt{9.9}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.05}}{\mathtt{\,\times\,}}{\mathtt{23.9}}{\mathtt{\,\times\,}}{\mathtt{2}}\right){\mathtt{\,\times\,}}{\mathtt{0.5}} = {\mathtt{0}}$$

$$\left({\mathtt{0.05}}{\mathtt{\,\times\,}}\left(-{\mathtt{38.1}}\right){\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.2}}{\mathtt{\,\times\,}}\left(-{\mathtt{26.1}}\right){\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.5}}{\mathtt{\,\times\,}}\left({\mathtt{7.9}}\right){\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.2}}{\mathtt{\,\times\,}}\left({\mathtt{9.9}}\right){\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.05}}{\mathtt{\,\times\,}}\left({\mathtt{23.9}}\right){\mathtt{\,\times\,}}{\mathtt{2}}\right){\mathtt{\,\times\,}}{\mathtt{0.5}} = {\mathtt{0}}$$

It looks like you took off the 2's after each set of parentheses from step 2 to step 3, Melody.

Maybe he meant these to be ^2? I'm not sure. Could be possible.

Thanks Ninja,

A lot of things could have been meant but what is annoying me is that I did it on the calc and I did it myself.  The same question was being answered both times but they are not the same and I have not been able to spot where I went wrong.  

Hm..can't really help you with that.

Hope you get that figured out. :)

It doesn't matter, it is just a little annoying.  If I wanted to find it badly enough then i would.

Yes probably.