https://file.aiquickdraw.com/mathbot/file/17260146725041ru9ccsn.jpg

Let's simplify both expressions provided in the image.

### a. \(\left( \dfrac{3p^2q}{q^{-1}} \right)^{-1}\)

#### Step 1: Simplify the fraction inside the parentheses.
\[
\dfrac{3p^2q}{q^{-1}} = 3p^2q^{1 - (-1)} = 3p^2q^2
\]

#### Step 2: Apply the exponent \(-1\) to the entire expression.
\[
\left( 3p^2q^2 \right)^{-1} = \dfrac{1}{3p^2q^2}
\]

Thus, the simplified form is:
\[
\boxed{\dfrac{1}{3p^2q^2}}
\]

---

### b. \(\dfrac{2x^3y^{-2}}{4x^2y}\)

#### Step 1: Simplify the coefficients.
\[
\dfrac{2}{4} = \dfrac{1}{2}
\]

#### Step 2: Simplify the powers of \(x\) and \(y\).
For \(x\):
\[
\dfrac{x^3}{x^2} = x^{3-2} = x^1 = x
\]
For \(y\):
\[
\dfrac{y^{-2}}{y^1} = y^{-2-1} = y^{-3}
\]

#### Step 3: Combine everything.
\[
\dfrac{2x^3y^{-2}}{4x^2y} = \dfrac{1}{2} \cdot x \cdot y^{-3} = \dfrac{x}{2y^3}
\]

Thus, the simplified form is:
\[
\boxed{\dfrac{x}{2y^3}}
\]

---

Would you like further explanation on any of these steps?

Here are 5 related questions you might explore:
1. How do you simplify expressions with negative exponents?
2. What happens when you multiply and divide powers with the same base?
3. How do fractional coefficients affect the simplification process?
4. Can you apply the same process to more complex rational expressions?
5. What is the role of the reciprocal in simplifying expressions raised to negative exponents?

**Tip:** Always apply exponent rules carefully when dealing with negative powers, especially when combining terms in fractions.

Sederhanakan notasi bilangan berpangkat berikut: a. (3p^2q / q^{-1})^{-1}, b. (2x^3y^{-2}) / (4x^2y)

Learn how to simplify exponent expressions with negative exponents, such as (3p^2q / q^{-1})^{-1} and (2x^3y^{-2}) / (4x^2y), using exponent rules. Suitable for students in Grades 9-10.

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