Question

check for extraneous solutions. 0, 7^4 2^4, inside the equation x^5/6 = 9x^7/12 - 14x^1/3

Answer 1

the solutions you plug in are 0, 7^4, and 2^4

Answer 2

well, 0 obviously works

(2^4)^5/6 = 2^10/3 = 2^3*2^1/3 = 8*2^1/3
9(2^4)^7/12 = 9*2^7/3 = 36*2^1/3
14(2^4)^1/3 = 14*2^4/3 = 28*2^1/3
8=36-28

looks good to me

You can check 7^4 in a similar manner.