Evaluate the radical expression by hand a 232 middot 2123 b

Evaluate the radical expression by hand. a) (2^-3/2 middot 2^1/2)^-3 b) (4/6)^-3/2

Solution

(a) ( 2^-3/2 * 2^1/2)^-3 = (2^-3/2+1/2)^-3 = (2^-1)^-3 = 2³ = 8 [ as a^p * a^q = a^p+q and (a^m)ⁿ = a^mn]

(b) (4/6)^-3/2 = (2/3)^-3/2 = (3/2)^3/2 = 3^3/2/2^3/2 =( 3*3^1/2)/(2 *2^1/2) = (33)/(22) = (3/2)* (3/2)