256=r^4

Solution for 256=r^4 equation:

Simplifying
256 = r4

Solving
256 = r4

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1r4' to each side of the equation.
256 + -1r4 = r4 + -1r4

Combine like terms: r4 + -1r4 = 0
256 + -1r4 = 0

Add '-256' to each side of the equation.
256 + -256 + -1r4 = 0 + -256

Combine like terms: 256 + -256 = 0
0 + -1r4 = 0 + -256
-1r4 = 0 + -256

Combine like terms: 0 + -256 = -256
-1r4 = -256

Divide each side by '-1'.
r4 = 256

Simplifying
r4 = 256

Reorder the terms:
-256 + r4 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + r4 = 0

Factor a difference between two squares.
(16 + r2)(-16 + r2) = 0

Factor a difference between two squares.
(16 + r2)((4 + r)(-4 + r)) = 0

Subproblem 1
Set the factor '(16 + r2)' equal to zero and attempt to solve:

Simplifying
16 + r2 = 0

Solving
16 + r2 = 0

Move all terms containing r to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + r2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + r2 = 0 + -16
r2 = 0 + -16

Combine like terms: 0 + -16 = -16
r2 = -16

Simplifying
r2 = -16

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Subproblem 3
Set the factor '(-4 + r)' equal to zero and attempt to solve:

Simplifying
-4 + r = 0

Solving
-4 + r = 0

Move all terms containing r to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + r = 0 + 4
r = 0 + 4

Combine like terms: 0 + 4 = 4
r = 4

Simplifying
r = 4
Solution
r = {-4, 4}