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= (2^5)^(2/3)
= 2^(10/3)
b) 1024^2/5
= (2^10)^2/5
= 2^4
= 16
c) (81/1000)^1/4
= ((3/10)^4)^1/4
= 3/10
d) (-243)^2/5
= ((-3)^5)^2/5
= (-3)^2
= 9
e) ((5^1/2 x 5^-1))^1/4
= 5^1/8 x 5^-1/4
= 5^(1/8 - 2/8)
= 5^(-1/8)
f) 5^2/4 x 4^2/4 x 4^1/4
= (20)^2/4 x 4^1/4
g) 32^3/4 : 32^1/4
= 32^(3/4 - 1/4)
= 32^2/4
= 32^1/2
= 2^5/2
h) (x/y^1/5) : x^1/3 y^1/5
= x^(1 - 1/3)
= x^2/3
i) (1/2^6)^1/4
= 1/2^(3/2)
j) (64/1000)^1/4
= 2^(3/2) / 10^(3/4)
k) x^2 / y^3
l) - 8/27 a^4 b^6