The algebraic expression \((pq^{-1})^4\) can be simplified step by step.

### Step-by-Step Simplification:

1. **Rewrite the term \( pq^{-1} \):**
   \[
   pq^{-1} = \frac{p}{q}
   \]
   This is because \( q^{-1} \) is the same as \( \frac{1}{q} \).

2. **Apply the exponent to the entire expression:**
   \[
   (pq^{-1})^4 = \left( \frac{p}{q} \right)^4
   \]

3. **Distribute the exponent across the fraction:**
   \[
   \left( \frac{p}{q} \right)^4 = \frac{p^4}{q^4}
   \]

Thus, the simplified expression is:
\[
\frac{p^4}{q^4}
\]

### Final Answer:
\[
(pq^{-1})^4 = \frac{p^4}{q^4}
\]

Would you like more details or have any further questions?

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Here are 5 related questions for practice:
1. Simplify \( (ab^{-1})^3 \).
2. What is the value of \( (xy^{-1})^2 \) when \( x = 3 \) and \( y = 2 \)?
3. Simplify \( (m^2 n^{-3})^2 \).
4. How would you simplify \( (p^{-1} q)^5 \)?
5. Expand \( (2p^2 q^{-3})^3 \).

**Tip:** When raising a fraction to a power, both the numerator and denominator are raised to that power separately.

Discover how to simplify the algebraic expression (pq⁻¹)⁴ step by step, using exponent and fraction rules. This guide breaks down the process and explains key algebraic concepts, suitable for students in Grades 8-10.

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