>>79459
Goddamn that's small, I apologize. The index number is 3.

Are you funking kidding? You can't solve this their is not enough data. If anything you can only find the sq root of 108

>>79465
I apologize, I forgot to mention I need to simplify it, leaving it as 1 term in simplest radical form. I'm not good at this.

>>79466
3 times the sq root of 108 times c to the 7th times d to the 4th times f to the 9th if you want it as one term then its whatever the sq root of 108 times C times D times F but what I'm guessing is you want it as one unit/number which is then 3=the sq root of 108 then you divide that by C which is whatever the sq root of 108C which is then to the blank power so if the sq root of 108 is 2 then its 2 to the 7th (which is 2x2x2x2x2x2) so its that number in place of the former c to the 7th then you do the same with D and F

>>79466
Example:
3√108c7 x d4 x f9
3√ sq÷c7= sq7 sq÷d4=sq4 sq÷f9=sq9
Then the problem becomes
3√answer of sq7 x sq4 x sq9 = answer to the power of 3 meaning the 3rd power of the answer

Just to help you √10.3923048
Good luck

Call me crazy, but isn't the answer simply:

(4.762) x c^(7/3) x d^(4/3) x f^3

>>79750
or you can write terms outside of the cubic root:

108 = 4⋅27 => 108^(1/3) = 3(4)^(1/3)

(108 c^7 d^4 f^9)^(1/3) = 3 c^2 d f^3 (4cd)^(1/3)

>>79459
108=3^3 2^2

∛108c^7d^4f^9 = ∛108 ∛c^7 ∛d^4 ∛f^9 = 3∛4 c^2∛c d∛d f^3 = 3c^2df^3∛4cd