These are not equalities but approximations
do you mean [1 - (200/1000)^1/10] x 100?
parentheses first, so 200/1000 = 0.2
exponents next, so .2^(1/10) = 0.851339923
next parentheses, so 1 - 0.851339923 = 0.148660077
lastly multiply by 100, so 0.148660077 x 100 = 14.8660077 or 14.87, but I guess they rounded off differently and got 14.86
I'm just going to add real quick that this problem is just to see if you can correctly use orders of operation. Remember PEMDAS?
Please Excuse My Dear Aunt Sally
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Move from left to right in the equation once these have been satisfied