solve for x

Solve for S:
1/S^0.75 = 0.1

1/S^0.75 = 1/S^(3/4) and 0.1 = 1/10:
S^(-3/4) = 1/10

Take reciporicals of both sides:
S^(3/4) = 10

Raise both sides to the power of four:
S^3 = 10000

Taking cube roots gives 10 10^(1/3) times the third roots of unity:
S = -10 (-10)^(1/3) or S = 10 10^(1/3) or S = 10 (-1)^(2/3) 10^(1/3)

1/S^0.75 => 1/(-10 (-10)^(1/3))^0.75 ~~ 0.1 i
0.1 => 0.1 ~~ 0.1:
So this solution is incorrect

1/S^0.75 => 1/(10 10^(1/3))^0.75 ~~ 0.1
0.1 => 0.1 ~~ 0.1:
So this solution is correct

1/S^0.75 => 1/(10 (-1)^(2/3) 10^(1/3))^0.75 ~~ -0.1 i
0.1 => 0.1 ~~ 0.1:
So this solution is incorrect

The solution is:
Answer: | 
| S = 10 10^(1/3)=21.544

S ≈ 21.5