how can i solve x^4=81

Since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

The inverse (opposite operation) of "to the fourth power" is "to the fourth root".

   (x^4) ^ ¼  = 81 ^ ¼ 

   81 = 3^4    so (3 ^ 4) ^ ¼  =   3 ^ 1   = 3

By hand: (3 ^ 4) ^ ¼  =  3 ^ (4 x ¼) = 3 ^ 1  = 3   (When you take a power to a power, multiply the exponents.)

Or, do it by calculator. One way of finding the fourth root is to use ^ (1/4)

3to4=81 

Another possibility is to simply subtract 81 from both sides. This gives

x^4 - 81 = 0     factor

(x^2 + 9) (x^2 - 9) = 0

If we set both factors = to 0, the first has no real solution. By factoring again, the second gives us

(x + 3) (x - 3) = 0

And the solutions are -3 and 3