Question

How do you simplify `(2^(1/6) * 2^(1/3)) ^(3/2)`?

Answer 1

I found: `root4(8)`

Explanation:

You can use the following facts:
`x^a*x^b=x^(a+b)`
`(x^a)^b=x^(a*b)`
So you get:
`(2^(1/6+1/3))^(3/2)=(2^(3/6))^(3/2)=(2^(1/2))^(3/2)=`
`=2^(1/2*3/2)=2^(3/4)=root4(2^3)=root4(8)`