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.

It's just above the ÷ 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.

On a TI-83 Plus calculator, the x^y key represents the exponentiation operation (raising a number to a power). To find the x^y key, follow these steps:

1. Turn on your TI-83 Plus calculator.
2. Locate the "^" key on the keypad. It is usually located above the "ENTER" key or next to the numerical keypad.
3. Press the number you want to raise to a power, for example, "A".
4. Press the "^" key.
5. Enter the power you want to raise "A" to, in this case, "7".
6. Press the "ENTER" key to calculate the value of "Pa^7".

Now, let's calculate f(7) using the given values:

1. Start with the initial values:
- A = (109/3)^1/4
- P = 3

2. Calculate "Pa^7":
- Press the following keys in sequence: "3", "x", "A", "x^y", "7"
- The calculator will perform the calculation and display the result.

To find the difference between the rounded value of 1831 and the calculated result, follow these steps:

1. Subtract the rounded value from the calculated result:
- Calculate 1831 - (the calculated result from the previous step).
- The difference will show the error introduced by rounding the value of "A".

Note: To round the value of "A" to 1831, you can use the "round" function on your calculator. However, the specifics may vary depending on the calculator model you are using.