To simplify the expression $\left( (p)^{\frac{3}{2}} \right)^{-2}$, follow these steps:

Step 1: Apply the power of a power rule

The power of a power rule states that $\left( a^m \right)^n = a^{m \cdot n}$. So, applying this to the expression:

$\left( p^{\frac{3}{2}} \right)^{-2} = p^{\frac{3}{2} \cdot (-2)} = p^{-3}$

Step 2: Simplify the exponent

$p^{-3}$

Step 3: Convert the negative exponent to a fraction

Using the rule $a^{-n} = \frac{1}{a^n}$, we rewrite $p^{-3}$ as:

$p^{-3} = \frac{1}{p^3}$

Thus, the simplified form of $\left( (p)^{\frac{3}{2}} \right)^{-2}$ is:

$\boxed{\frac{1}{p^3}}$

Let me know if you'd like further details or have questions!

Related Questions:

1. How do you simplify expressions involving fractional exponents?
2. What is the power of a power rule in exponents?
3. Can you explain the meaning of negative exponents in more depth?
4. How does the rule $a^{-n} = \frac{1}{a^n}$ work in general?
5. What happens when you raise a product to a fractional exponent?

Tip: Always simplify exponents step by step, especially when dealing with fractional and negative powers.