The expression in the image appears to be a rational function involving powers of $10$ and $t$. Specifically, it looks like this:

$\frac{10t^{-9}}{(10t^9)(t)}$

To simplify this expression, we will break it down:

1. Numerator: $10t^{-9}$
2. Denominator: $(10t^9)(t) = 10t^{9+1} = 10t^{10}$

Now the expression becomes:

$\frac{10t^{-9}}{10t^{10}}$

Since both the numerator and denominator have a factor of $10$, they can be canceled out. We are left with:

$\frac{t^{-9}}{t^{10}}$

Using the exponent rule $\frac{t^a}{t^b} = t^{a-b}$, we simplify further:

$t^{-9 - 10} = t^{-19}$

So, the simplified form of the given expression is:

$t^{-19}$

Would you like to go into more detail or need further clarification on any steps?

Here are 5 related questions you might find interesting:

1. How do we handle negative exponents in expressions?
2. What are the rules for simplifying expressions with powers of variables?
3. How do we simplify complex fractions in algebra?
4. What are the basic exponent laws that can be used in algebraic simplification?
5. How can we apply exponent rules in real-life mathematical problems?

Tip: Always remember that $t^{-a} = \frac{1}{t^a}$ when simplifying expressions with negative exponents!