Question 741984
Take the 7th root of both sides.

On the TI-84, enter the following keystrokes:

On the home screen, type the number 7; then, go to MATH
MATH (found under the Alpha (green tab) key): select option #5 and type 823,543
hit enter and you get 7

So, 7^7 = 7*7*7*7*7*7*7 = 823,543