Find the simplified product. it’s in the attached and explain it. i tried to solve this multiple times and i don’t get it right

3x³y √(5xy)

Step-by-step explanation:

√(3x⁴y) √(15x³y²)

Multiply the radicands.  When multiplying, add the exponents (xᵃ xᵇ = xᵃ⁺ᵇ).

√(45x⁴⁺³y¹⁺²)

√(45x⁷y³)

To simplify further, we need to factor out perfect squares (anything with an even exponent).

√(3²·5 x⁶x y²y)

√(3²x⁶y²) √(5xy)

Take the square root of the perfect square (halve the exponent).

3x³y √(5xy)