The expression shown in the image is:

$\left(\frac{p^3 q^6}{a^4 b^{-2}}\right) \left(\frac{ab}{p^3 q}\right)$

Step 1: Multiply the numerators and the denominators.

Let's multiply the expressions:

$\frac{p^3 q^6 \cdot ab}{a^4 b^{-2} \cdot p^3 q}$

Step 2: Simplify the expression.

• For the $p$ terms: $p^3$ in the numerator and $p^3$ in the denominator cancel out.
• For the $q$ terms: $q^6$ in the numerator and $q$ in the denominator simplify to $q^{6-1} = q^5$.
• For the $a$ terms: $a$ in the numerator and $a^4$ in the denominator simplify to $a^{1-4} = a^{-3}$.
• For the $b$ terms: $b$ in the numerator and $b^{-2}$ in the denominator simplify to $b^{1+2} = b^3$.

Now, the simplified expression is:

$\frac{q^5 b^3}{a^3}$

Thus, the simplified form of the expression is:

$\frac{q^5 b^3}{a^3}$

Would you like further details or have any questions?

Here are some related questions:

1. How would the expression change if $p$ was raised to a different power?
2. What if the exponents for $a$ and $b$ were negative in the numerator instead?
3. How can this expression be used in solving real-world problems?
4. What happens if all variables $p$, $q$, $a$, and $b$ were equal to 1?
5. How would you differentiate this expression with respect to $q$?

Tip: When simplifying algebraic expressions with exponents, always combine like terms and carefully handle the signs of exponents.