The expression $\left( \frac{p^3}{2} \right)^{-2}$ can be simplified using the rules of exponents. Here's the step-by-step process:

1. Apply the exponent rule $\left( \frac{a}{b} \right)^n = \frac{a^n}{b^n}$: $\left( \frac{p^3}{2} \right)^{-2} = \frac{\left( p^3 \right)^{-2}}{2^{-2}}$

2. Simplify each part:

   • For the numerator: $\left( p^3 \right)^{-2} = p^{3 \times (-2)} = p^{-6}$
   • For the denominator: $2^{-2} = \frac{1}{2^2} = \frac{1}{4}$

   This gives: $\frac{p^{-6}}{\frac{1}{4}} = p^{-6} \times 4$

3. Finally, simplify the result: $4p^{-6} = \frac{4}{p^6}$

So, $\left( \frac{p^3}{2} \right)^{-2} = \frac{4}{p^6}$.

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. How would you simplify $\left( \frac{p^2}{3} \right)^{-3}$?
2. What happens when you apply a positive exponent instead of a negative one?
3. Can you simplify $\left( \frac{p^5}{4q^3} \right)^{-2}$?
4. How does the rule $(ab)^n = a^n b^n$ help simplify expressions like $\left( \frac{p^4}{6} \right)^3$?
5. How would the answer change if $p$ had a coefficient in front of it, like $2p^3$?

Tip: When dealing with negative exponents, remember that they indicate reciprocation of the base.