# Solve for z (z-1)^4=81 (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
Simplify the right side of the equation.
Rewrite 81 as 34.
z-1=±344
Pull terms out from under the radical, assuming positive real numbers.
z-1=±3
z-1=±3
The complete solution is the result of both the positive and negative portions of the solution.
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

### Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top