Question

Solve the equation with rational exponents
(x-1)3/2=27

Answer 1

$~~~~~~(x-1)^{\tfrac 32} =27\\\\\implies \left[(x-1)^{\tfrac 12} \right]^3 = 3^3\\\\\implies (x-1)^{\tfrac 12} = 3~~~~~~~~~;[\text{Cube root on both sides}]\\\\\implies x -1 = 9~~~~~~~~~~~~;[\text{Square both sides}]\\\\\implies x = 10$