Let's focus on the cube root of 81 first. What's the prime factorisation of 81? It's simply: 3 * 3 * 3 * 3, or . Put this in for 81:
We know that the cube root of 3 cubed will cancel out to become 3, but the cube root of 3 cannot be further simplified, so we keep that. Our outcome is then:
Now, let's multiply this by 1/3, as shown in the original problem:
The total number of ratio units in 6:5 is 6+5=11, so each of those ratio units must stand for 550/11 = 50 detectives. Then the 6 ratio units of police detectives stand for 6·50 = 300 police detectives.