The expression in the image is:

$\frac{p^{-2}}{-2^{-1} q^{-10}}$

Let's simplify this step-by-step:

Step 1: Simplify the negative exponents

1. $p^{-2}$ can be rewritten as $\frac{1}{p^2}$.
2. $-2^{-1}$ can be rewritten as $-\frac{1}{2}$.
3. $q^{-10}$ can be rewritten as $\frac{1}{q^{10}}$.

So the expression becomes:

$\frac{\frac{1}{p^2}}{-\frac{1}{2} \cdot \frac{1}{q^{10}}}$

Step 2: Multiply the fractions

The denominator $-\frac{1}{2} \cdot \frac{1}{q^{10}}$ becomes $-\frac{1}{2q^{10}}$.

So now the expression is:

$\frac{\frac{1}{p^2}}{-\frac{1}{2q^{10}}}$

Step 3: Dividing by a fraction

To divide by a fraction, multiply by its reciprocal. So, this becomes:

$\frac{1}{p^2} \times \frac{-2q^{10}}{1} = \frac{-2q^{10}}{p^2}$

Thus, the simplified form of the expression is:

$\boxed{\frac{-2q^{10}}{p^2}}$

Would you like further details or explanations on any of the steps?

Here are five related questions you might find helpful:

1. How do negative exponents affect the base in an expression?
2. How do you divide fractions with variables in both the numerator and denominator?
3. What is the rule for multiplying expressions with the same base but different exponents?
4. How do you simplify expressions involving products of powers?
5. What happens when you raise a fraction to a negative exponent?

Tip: When working with negative exponents, remember they simply represent the reciprocal of the base raised to the positive exponent.