A Utility Function Is Given By $U = x _ { 1 } ^ { \frac { 2 } { 3 } } x _ { 2 } ^ { \frac { 1 } { 2 } }$

Multiple Choice

A utility function is given by $U = x _ { 1 } ^ { \frac { 2 } { 3 } } x _ { 2 } ^ { \frac { 1 } { 2 } }$ Find the value of x2 if the points, (64, 256) and (512, x2) lie on the same indifference curve.

A) 64
B) 4
C) 16
D) 256
E) 1024