Answer:
11sqrt(33)
------------
9
Step-by-step explanation:
(11/3)^(3/2)
Apply the cube to inside:
(11^3/3^3)^(1/2)
Recall (x^3)^(1/2)=sqrt(x^3)=sqrt(x^2)×sqrt(x)=x×sqrt(x)
So we have:
11sqrt(11)
------------
3sqrt(3)
Rationalize denominator by multiplying top and bottom by sqrt(3):
11sqrt(11)sqrt(3)
------------
3sqrt(3)sqrt(3)
=
11sqrt(33)
------------
3(3)
=
11sqrt(33)
------------
9
