how to simplify radical

Question

attached i couldnt write out

 

http://assets.openstudy.com/updates/attachments/5547b51fe4b0868da1bf0432-nickymail48-1430762796293-jk.png

Answer 1

For this problem, you'll use the fact that ⁿ√(a^m) = (ⁿ√a)^m = a^(m/n). A normal square root sign means n = 2.

 

 

Applying that rule:

 

√(a³) = a^(3/2)

³√(a²) = a^(2/3)

 

 

Together, that means that:

 

√(a³)(³√(a²)) = a^(3/2)a^(2/3)

 

 

Remember that a^xa^y = a^x+y. Therefore:

 

a^(3/2)a^(2/3) = a^(9/6)a^(4/6) = a^(13/6)

 

 

You can put that back into radical form if you'd like:

 

⁶√(a¹³)