Solve the equation with rational exponents x 532 64 Select

Solve the equation with rational exponents. (x - 5)^3/2 = 64 Select the correct choice below and. if necessary, fill in the answer box The solution set is The solution set is the empty set.

Solution

(x-5)^3/2=64

squaring on both sides

((x-5)^3/2)²=64²

(x-5)³=64²

by law of exponents :a^m=b =>a=b^1/m

(x-5)=64^2/3

(x-5)=(4³)^2/3

(x-5)=(4)²

x-5=16

x=16+5

x=21

solution is x =21