Simplify with only positive exponents:

(v^-1/2t)^-2(t^2/v^-2)^-3

To simplify the given expression with positive exponents, we can start by using the exponent rules. Let's break it down step by step:

1. Evaluate the exponents inside the parentheses:
- For the expression (v^(-1/2)t)^-2, we can first simplify the exponent by multiplying it with -2:
v^(-1/2 * -2)t^(-2) = v^1t^(-2) = vt^(-2).

- For the expression (t^2/v^(-2))^-3, we can simplify the exponent by multiplying it with -3:
(t^2/v^(-2))^(-3) = t^(2 * -3)/v^(-2 * -3) = t^(-6)/v^6.

2. Combine the simplified expressions:
Now, we can combine the two expressions obtained in the previous step:
(vt^(-2)) * (t^(-6)/v^6) = vt^(-2) * t^(-6)/v^6.

3. Simplify using the exponent rule for multiplication:
When multiplying terms with the same base, we add the exponents:
vt^(-2) * t^(-6) = v * t^(-2 + -6) = v * t^(-8) = v/t^8.

Therefore, the simplified expression with only positive exponents is v/t^8.