The question asks to simplify the expression:

$(-3z^2y)(5z^3y^2)$

Solution:

1. Combine the coefficients: $-3 \cdot 5 = -15$

2. Add the powers of $z$: $z^2 \cdot z^3 = z^{2+3} = z^5$

3. Add the powers of $y$: $y \cdot y^2 = y^{1+2} = y^3$

Thus, the simplified expression is:

$-15z^5y^3$

This matches option C.

5 Related Problems:

1. Simplify: $(-2x^3y^2)(4x^5y^3)$
2. Simplify: $(3a^4b)(-5a^2b^3)$
3. Simplify: $(-7p^2q^3)(2p^5q)$
4. Simplify: $(6x^2y^3)(-x^4y^2)$
5. Simplify: $(-5m^3n^2)(-4m^2n^3)$

Tip:

When multiplying powers of the same base, always add the exponents.