Simplifying various algebraic expressions

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Notation:
^ means to the power of
sqrt(.) means square root of (.)
1|1/2 means 1 and a half, i.e. 3/2

Some of the algebraic properties that I will use:
i) a^(b*c) = (a^b)^c , e.g. a^8 = (a^4)^2 = (a^2)^4 (they are interchangeable)
ii) n-th root of (a) = a^(1/n), e.g. 3-rd root of 8 = 8^(1/3) = 2
iii) 1/a = a^(-1), e.g. 1/(x^4) = (x^4)^(-1) = x^(-4)

2a) sqrt(64 x^8 y^12) = sqrt( 8^2 (x^4)^2 (y^6)^2) by property i)
= 8 x^4 y^6 by property ii)

2b) 3rd-root(2^3 (x^2)^3 (y^5)^3) = 2 x^2 y^5 using properties i) and ii)

3a) ...