Question 1061724
I am assuming the problem is 5*sqrt(-32)/5* sqrt (243). Cancel the 5 right away
The numerator is i sqrt(32), but sqrt (32)=sqrt (16)*sqrt (2)=4 sqrt (2)
4i sqrt (2)
divided by  sqrt (243)
243=3^5
Therefore sqrt (3^5) is sqrt (3*3*3*3*3)=3*3*sqrt (3)=9 sqrt (3)
The answer is 
4i sqrt (2)/9 sqrt (3)
rationalize the denominator by multiplying top and bottom by sqrt (3)
4i sqrt(6)/9*3
4i sqrt (6)/27