(y^8)=y^40

Solution for (y^8)=y^40 equation:

Simplifying
(y8) = y40
y8 = y40

Solving
y8 = y40

Solving for variable 'y'.

Combine like terms: y40 + -1y40 = 0
y8 + -1y40 = 0

Factor out the Greatest Common Factor (GCF), 'y8'.
y8(1 + -1y32) = 0

Factor a difference between two squares.
y8((1 + y16)(1 + -1y16)) = 0

Factor a difference between two squares.
y8((1 + y16)((1 + y8)(1 + -1y8))) = 0

Factor a difference between two squares.
y8((1 + y16)((1 + y8)((1 + y4)(1 + -1y4)))) = 0

Factor a difference between two squares.
y8((1 + y16)((1 + y8)((1 + y4)((1 + y2)(1 + -1y2))))) = 0

Factor a difference between two squares.
y8((1 + y16)((1 + y8)((1 + y4)((1 + y2)((1 + y)(1 + -1y)))))) = 0

Subproblem 1
Set the factor 'y8' equal to zero and attempt to solve:

Simplifying
y8 = 0

Solving
y8 = 0

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

Simplifying
y8 = 0

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 '(1 + y16)' equal to zero and attempt to solve:

Simplifying
1 + y16 = 0

Solving
1 + y16 = 0

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

Add '-1' to each side of the equation.
1 + -1 + y16 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + y16 = 0 + -1
y16 = 0 + -1

Combine like terms: 0 + -1 = -1
y16 = -1

Simplifying
y16 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + y8)' equal to zero and attempt to solve:

Simplifying
1 + y8 = 0

Solving
1 + y8 = 0

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

Add '-1' to each side of the equation.
1 + -1 + y8 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + y8 = 0 + -1
y8 = 0 + -1

Combine like terms: 0 + -1 = -1
y8 = -1

Simplifying
y8 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 4
Set the factor '(1 + y4)' equal to zero and attempt to solve:

Simplifying
1 + y4 = 0

Solving
1 + y4 = 0

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

Add '-1' to each side of the equation.
1 + -1 + y4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + y4 = 0 + -1
y4 = 0 + -1

Combine like terms: 0 + -1 = -1
y4 = -1

Simplifying
y4 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 5
Set the factor '(1 + y2)' equal to zero and attempt to solve:

Simplifying
1 + y2 = 0

Solving
1 + y2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + y2 = 0 + -1
y2 = 0 + -1

Combine like terms: 0 + -1 = -1
y2 = -1

Simplifying
y2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 6
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

Combine like terms: 1 + -1 = 0
0 + y = 0 + -1
y = 0 + -1

Combine like terms: 0 + -1 = -1
y = -1

Simplifying
y = -1
Subproblem 7
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1y = 0 + -1
-1y = 0 + -1

Combine like terms: 0 + -1 = -1
-1y = -1

Divide each side by '-1'.
y = 1

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