a) To solve the equation (x-1)^3 - 1/27 = 0, we can start by rewriting it as:

(x-1)^3 = 1/27

Now, we can take the cube root of both sides to eliminate the exponent:

∛((x-1)^3) = ∛(1/27)

Simplifying the cube root of 1/27:

(x-1) = 1/3

Now, we can solve for x by adding 1 to both sides:

x = 1/3 + 1

x = 4/3

So the solution to the equation (x-1)^3 - 1/27 = 0 is x = 4/3.

b) To solve the equation (2x-1)^3 = 8, we can start by taking the cube root of both sides:

∛((2x-1)^3) = ∛8

Simplifying the cube root of 8:

2x-1 = 2

Now, we can solve for x by adding 1 to both sides and dividing by 2:

2x = 3

x = 3/2

So the solution to the equation (2x-1)^3 = 8 is x = 3/2.

I hope this helps! Let me know if you have any further questions.