x^4y^4-z^8=0

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Solution for x^4y^4-z^8=0 equation: 


Simplifying
x4y4 + -1z8 = 0

Solving
x4y4 + -1z8 = 0

Solving for variable 'x'.

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

Add 'z8' to each side of the equation.
x4y4 + -1z8 + z8 = 0 + z8

Combine like terms: -1z8 + z8 = 0
x4y4 + 0 = 0 + z8
x4y4 = 0 + z8
Remove the zero:
x4y4 = z8

Divide each side by 'y4'.
x4 = y-4z8

Simplifying
x4 = y-4z8

Combine like terms: y-4z8 + -1y-4z8 = 0
x4 + -1y-4z8 = 0

Factor a difference between two squares.
(x2 + y-2z4)(x2 + -1y-2z4) = 0

Factor a difference between two squares.
(x2 + y-2z4)((x + y-1z2)(x + -1y-1z2)) = 0


Subproblem 1
Set the factor '(x2 + y-2z4)' equal to zero and attempt to solve:

Simplifying
x2 + y-2z4 = 0

Solving
x2 + y-2z4 = 0

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

Add '-1y-2z4' to each side of the equation.
x2 + y-2z4 + -1y-2z4 = 0 + -1y-2z4

Combine like terms: y-2z4 + -1y-2z4 = 0
x2 + 0 = 0 + -1y-2z4
x2 = 0 + -1y-2z4
Remove the zero:
x2 = -1y-2z4

Simplifying
x2 = -1y-2z4

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 '(x + y-1z2)' equal to zero and attempt to solve:

Simplifying
x + y-1z2 = 0

Solving
x + y-1z2 = 0

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

Add '-1y-1z2' to each side of the equation.
x + y-1z2 + -1y-1z2 = 0 + -1y-1z2

Combine like terms: y-1z2 + -1y-1z2 = 0
x + 0 = 0 + -1y-1z2
x = 0 + -1y-1z2
Remove the zero:
x = -1y-1z2

Simplifying
x = -1y-1z2

Subproblem 3
Set the factor '(x + -1y-1z2)' equal to zero and attempt to solve:

Simplifying
x + -1y-1z2 = 0

Solving
x + -1y-1z2 = 0

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

Add 'y-1z2' to each side of the equation.
x + -1y-1z2 + y-1z2 = 0 + y-1z2

Combine like terms: -1y-1z2 + y-1z2 = 0
x + 0 = 0 + y-1z2
x = 0 + y-1z2
Remove the zero:
x = y-1z2

Simplifying
x = y-1z2
Solution
x = {-1y-1z2, y-1z2}

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