The expression you provided is:

$\frac{r^3 v^{-2}}{t^{-7}}$

To simplify this, we will use the laws of exponents.

1. When dividing exponents with the same base, subtract the exponents.
2. A negative exponent means the reciprocal of the base.

Now let's simplify the expression:

$\frac{r^3 v^{-2}}{t^{-7}} = r^3 \cdot v^{-2} \cdot t^7$

This simplifies to:

$r^3 \cdot \frac{t^7}{v^2}$

This is the simplest form of the given expression:

$\frac{r^3 t^7}{v^2}$

Would you like further details or have any other questions?

Here are some related questions you might explore:

1. How do you simplify expressions with exponents and fractions?
2. What is the rule for handling negative exponents?
3. How do exponents behave in multiplication and division?
4. Can you show how to simplify $\frac{a^4 b^{-3}}{c^{-2}}$?
5. What happens when both numerator and denominator have negative exponents?

Tip: Always remember that negative exponents indicate reciprocals!