I will do one of them, you show me what you have done so far for the others.
(4a^3 b^-1 c^-2)^1/2 ÷ [64(a^6 b^4 c^2)^-1/2]
= (2 a^(3/2)(b^(-1/2)(c-1) * (1/64)(a^3 b^2 c^-2)
= (1/32)(a^(9/2)(b^3/2)(c^-3)
= 1/32 √(a^9 b^3)
simplify each of the following in indices
a. s³÷t⁴ x (s-³ t-²)³
b. (4a^3 b^-1 c^-2)^1/2 ÷ [64(a^6 b^4 c^2)^-1/2]
c. 3√8a^3 b^6 ÷ √1/25 a⁴ b^7 * (16√a⁴b^6)^-1/2
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