I'm not sure when to use the absolute value sign when multiplying or dividing a radical even though I know the rules for absolute value of use it when it's even index.
I think you might be talking about something like this
√(y10) / √(y6)
Notice that we could simplify this as
l y5 l / l y3 l this would account for the fact that y might be negative
But notice .....if we just simplified the original thing as this
√(y10) / √(y6) = √(y10 / y6) √(y4) = y2
Then we don't have to worry about the absolute value signs at all....!!!
I think you might be talking about something like this
√(y10) / √(y6)
Notice that we could simplify this as
l y5 l / l y3 l this would account for the fact that y might be negative
But notice .....if we just simplified the original thing as this
√(y10) / √(y6) = √(y10 / y6) √(y4) = y2
Then we don't have to worry about the absolute value signs at all....!!!