Question 1051657
the fourth root of (x-7) is the same as (x-7)^(1/4)


equation becomes (x-7)^(1/4) = 2


raise both sides of the equation to the 4th power to get:


(x-7) = 2^4


simplify to get x - 7 = 16


add 7 to both sides to get x = 23


that's your solution.


confirm by replacing x with 23 in the original equation.


you get (23 - 7)^(1/4) = 2


simplify to get 16^(1/4) = 2


that's the same as the fourth root of 16 is equal to 2.


fourth root of 16 is equal to 2 and you get 2 = 2.


this confirms the solution is correct.


((x-7)^(1/4))^4 is the same as (x-7)^(1/4*4) which is equal to (x-7)^1 which is equal to x - 7.