r^4=1024

Solution for r^4=1024 equation:

Simplifying
r4 = 1024

Solving
r4 = 1024

Solving for variable 'r'.

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

Simplifying
r4 = 1024

Reorder the terms:
-1024 + r4 = 1024 + -1024

Combine like terms: 1024 + -1024 = 0
-1024 + r4 = 0

Factor a difference between two squares.
(32 + r2)(-32 + r2) = 0

Subproblem 1
Set the factor '(32 + r2)' equal to zero and attempt to solve:

Simplifying
32 + r2 = 0

Solving
32 + r2 = 0

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

Add '-32' to each side of the equation.
32 + -32 + r2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + r2 = 0 + -32
r2 = 0 + -32

Combine like terms: 0 + -32 = -32
r2 = -32

Simplifying
r2 = -32

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 '(-32 + r2)' equal to zero and attempt to solve:

Simplifying
-32 + r2 = 0

Solving
-32 + r2 = 0

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

Add '32' to each side of the equation.
-32 + 32 + r2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + r2 = 0 + 32
r2 = 0 + 32

Combine like terms: 0 + 32 = 32
r2 = 32

Simplifying
r2 = 32

Take the square root of each side:
r = {-5.656854249, 5.656854249}
Solution
r = {-5.656854249, 5.656854249}