when there is no number with redical sign here it is equivalent to the exponent " 1/2 "
but when it is 3 under redical x that means it is x^1/3
In first one 8 ^(9/2) is same as ( redical 8 ) ^9
In part B it is (3 under redical 125)^9 = ( 125 )^ 9/3 so this also same thing
In part C it is ( 12)^2/7) but the ( redical 12 ) ^7 is equal to ( 12)^7/2 so these two are not equivalent
in part D it is 4^1/5 but ( redical 4) ^5 = 4^( 5/2 which is also not equivalent
Answer : only A and B are equivalent