I need help understanding exponents
(a^1/2 b)^1/2 x (ab^1/2)
when you multiply, you add powers:
a^3 = a*a*a
a^5 = a*a*a*a
a^3 * a^5 = (a*a*a)(a*a*a*a*a) = a^8
similarly, when you raise powers to powers, you multiply them
(a^3)^2 = (a^3)(a^3) = a^(2*3) = a^6
(a^1/2 b)^(1/2) = a^(1/2 * 1/2) b^(1 * 1/2) = a^1/4 b^1/2
so, now you have
a^1/4 b^1/2 * a b^1/2
= a^(1/4 + 1) b^(1/2 + 1/2) = a^5/4 b