I compute (109/3)^1/4 and store that value in A.

Store 3 in P.
Now compute f(7)= Pa^7 by typing:

P x A x^y 7

***My problem is that I don't know WHERE the x^y key is on a TI -83 Plus.
Please help.

Then I have to subtract this answer from the answer using a rounded value of a (which I found to be 1831.)The difference will show the error used by rounding a and will not be zero.

3 answers

It's just above the รท button.

See:
http://www.google.ca/imgres?q=ti+83&hl=en&sa=X&biw=941&bih=645&tbm=isch&prmd=imvns&tbnid=tNE2Fcgtld_eNM:&imgrefurl=http://www.androidapps.com/tech/apps/533608-andy-83-doug-melton&docid=xkiKAfrXg5U0CM&imgurl=http://c1345842.cdn.cloudfiles.rackspacecloud.com/assets/screenshots/images/002/566/663/original.jpg%253F1298381046&w=480&h=800&ei=1di1TumgCMms2gW5y8nMDQ&zoom=1&iact=hc&vpx=495&vpy=241&dur=3483&hovh=290&hovw=174&tx=64&ty=312&sig=104651073321825125100&page=1&tbnh=197&tbnw=116&start=0&ndsp=12&ved=1t:429,r:9,s:0
So I punched it in and the calculator reads:

P * A ^ 7
1613.078231

Did I do it correctly?
Yes, I got the same answer.

The best way to check is to use numbers that you know, such as:
2^6=64,
2^20=1048576
3^4=81,
etc.