a^4=256

Solution for a^4=256 equation:

Simplifying
a4 = 256

Solving
a4 = 256

Solving for variable 'a'.

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

Simplifying
a4 = 256

Reorder the terms:
-256 + a4 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + a4 = 0

Factor a difference between two squares.
(16 + a2)(-16 + a2) = 0

Factor a difference between two squares.
(16 + a2)((4 + a)(-4 + a)) = 0

Subproblem 1
Set the factor '(16 + a2)' equal to zero and attempt to solve:

Simplifying
16 + a2 = 0

Solving
16 + a2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + a2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + a2 = 0 + -16
a2 = 0 + -16

Combine like terms: 0 + -16 = -16
a2 = -16

Simplifying
a2 = -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 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

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

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

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

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

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

Simplifying
-4 + a = 0

Solving
-4 + a = 0

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

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

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

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

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