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.

Learn how to simplify the expression (p^(3/2))^-2 by applying the power of a power rule and converting negative exponents. This detailed guide walks you through each step, using key concepts like fractional and negative exponents. Suitable for students in Grades 9-12.

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