\binom{ \sqrt[6]{s} * \sqrt{ {s}^(9) } } { \sqrt{16 {s}^(18) } } sixth root of s times square root of s to the 9th divided by square root of 16 times s to the 18th

Question

`\binom{ \sqrt[6]{s} * \sqrt{ {s}^(9) } } { \sqrt{16 {s}^(18) } }`

sixth root of s
times
square root of s to the 9th
divided by
square root of 16 times s to the 18th

Answer 1

Quick note: the
`\dbinom xy` expression you used is misleading and not the same as
`\frac xy`.

The notations
`\sqrt[n]s` and
`s^(1/n)` are equivalent in this context:

`\frac{\sqrt[6]s√(s^9)}{\sqrt{16s^(18)}}=(s^(1/6)s^(9/2))/(√(16)s^(18/2))=(s^(1/6+9/2))/(4s^9)=(s^(14/3))/(4s^9)=\frac{s^(-13/3)}4=\frac4{s^(13/3)}=\frac4{\sqrt[3]{s^(13)}}`