Question

How do you simplify `(6^(1/2) * 6^(3/2))^ (4/3)`?

Answer 1

`(6^(1/2)*6^(3/2))^(4/3)=(6^(1/2+3/2))^(4/3)`

`=(6^2)^(4/3)=6^(2*4/3)`

`=6^(8/3)`

...using the properties of exponentials:

`a^b*a^c = a^(b+c)`

`(a^b)^c = a^(bc)`