16a^8-1=0

Solution for 16a^8-1=0 equation:

Simplifying
16a8 + -1 = 0

Reorder the terms:
-1 + 16a8 = 0

Solving
-1 + 16a8 = 0

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + 16a8 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 16a8 = 0 + 1
16a8 = 0 + 1

Combine like terms: 0 + 1 = 1
16a8 = 1

Divide each side by '16'.
a8 = 0.0625

Simplifying
a8 = 0.0625

Reorder the terms:
-0.0625 + a8 = 0.0625 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
-0.0625 + a8 = 0.0000

Factor a difference between two squares.
(0.25 + a4)(-0.25 + a4) = 0.0000

Factor a difference between two squares.
(0.25 + a4)((0.5 + a2)(-0.5 + a2)) = 0.0000

Subproblem 1
Set the factor '(0.25 + a4)' equal to zero and attempt to solve:

Simplifying
0.25 + a4 = 0

Solving
0.25 + a4 = 0

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a4 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a4 = 0 + -0.25
a4 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
a4 = -0.25

Simplifying
a4 = -0.25

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 '(0.5 + a2)' equal to zero and attempt to solve:

Simplifying
0.5 + a2 = 0

Solving
0.5 + a2 = 0

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a2 = 0 + -0.5
a2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
a2 = -0.5

Simplifying
a2 = -0.5

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 '(-0.5 + a2)' equal to zero and attempt to solve:

Simplifying
-0.5 + a2 = 0

Solving
-0.5 + a2 = 0

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a2 = 0 + 0.5
a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
a2 = 0.5

Simplifying
a2 = 0.5

Take the square root of each side:
a = {-0.707106781, 0.707106781}
Solution
a = {-0.707106781, 0.707106781}