Let's solve the problems step by step based on the image provided:

---

32. $(5x^{-3})(-2y^3)$

To simplify:

• Multiply the coefficients:
  $5 \cdot -2 = -10$
• Since $x$ and $y$ are different variables, they remain separate.

Final answer:
$-10x^{-3}y^3$
(Note: If asked to write with positive exponents, rewrite as $-\frac{10y^3}{x^3}$).

---

33. $(-4a^4b^3)(2a^3b^2)(3ab)$

To simplify:

1. Multiply the coefficients:
   $-4 \cdot 2 \cdot 3 = -24$
2. Combine the powers of $a$:
   $a^4 \cdot a^3 \cdot a = a^{4+3+1} = a^8$
3. Combine the powers of $b$:
   $b^3 \cdot b^2 \cdot b = b^{3+2+1} = b^6$

Final answer:
$-24a^8b^6$

---

34. $(a^2b^4)(a^3b)(-3b^2)$

To simplify:

1. Multiply the coefficients:
   $1 \cdot 1 \cdot -3 = -3$
2. Combine the powers of $a$:
   $a^2 \cdot a^3 = a^{2+3} = a^5$
3. Combine the powers of $b$:
   $b^4 \cdot b \cdot b^2 = b^{4+1+2} = b^7$

Final answer:
$-3a^5b^7$

---

35. $(-r^4s^2t)(r^3s^2t^2)(-rst)$

To simplify:

1. Multiply the coefficients:
   $-1 \cdot 1 \cdot -1 = 1$
2. Combine the powers of $r$:
   $r^4 \cdot r^3 \cdot r = r^{4+3+1} = r^8$
3. Combine the powers of $s$:
   $s^2 \cdot s^2 \cdot s = s^{2+2+1} = s^5$
4. Combine the powers of $t$:
   $t \cdot t^2 \cdot t = t^{1+2+1} = t^4$

Final answer:
$r^8s^5t^4$

---

36. $(-3ab^2)(2a^3b)(-a^2b^2)(-2a^3b^2)$

To simplify:

1. Multiply the coefficients