What is a simplified form of 3√5c Times Square root of 15 C to the Third

The simplified form of 3√5c times the square root of 15c cubed is:

3√5c * √(15c)^3
= 3√5c * √(15^3 * c^3)
= 3√5c * √3375c^3
= 3 * (5)^1/3 * c * 15^(3/2) * c^(3/2)
= 3 * 5^(1/3) * 15^(3/2) * c^(1+3/2)
= 3 * 5^(1/3) * 15^(3/2) * c^(5/2)
= 3 * 5^(1/3) * 15^(3/2) * c^(5/2)
= 45 * ∛(75^2) * c^(5/2)
= 45 * √1125c^2
= 45√1125c^2.