Question

[a^1/3{a^1/2b^1/2(a^2b^2)^2/3}^-1/2]^4
here the fractions are the powers or exponents
i want a clear explanation

Answer 1

Consider, a^(1/2)b^(1/2)=(ab)^(1/2) and (a²b²)^{2/3}=(ab)^(4/3) There product is (ab)^{1/2 + 4/3}=(ab)^{11/6}. (ab)^{(11/6)*(-1/2)}=(ab)^{-11/12} Hence, (a^(1/3)*(ab)^{-11/12})^4=a^(-7/3)*b^(-11/3)