(z-1)4=81

Take the 4th root of each side of the equation to set up the solution for z

(z-1)4⋅14=±814

Remove the perfect root factor z-1 under the radical to solve for z.

z-1=±814

Rewrite 81 as 34.

z-1=±344

Pull terms out from under the radical, assuming positive real numbers.

z-1=±3

z-1=±3

First, use the positive value of the ± to find the first solution.

z-1=3

Move all terms not containing z to the right side of the equation.

Add 1 to both sides of the equation.

z=3+1

Add 3 and 1.

z=4

z=4

Next, use the negative value of the ± to find the second solution.

z-1=-3

Move all terms not containing z to the right side of the equation.

Add 1 to both sides of the equation.

z=-3+1

Add -3 and 1.

z=-2

z=-2

The complete solution is the result of both the positive and negative portions of the solution.

z=4,-2

z=4,-2

Solve for z (z-1)^4=81