Final answer:
To find the product of the square root of -3 cubed and the square root of -5 cubed, first simplify each expression by raising the number to the power and then taking the square root. Then, multiply the simplified expressions to find the product.
Step-by-step explanation:
To find the product of the square root of -3 cubed and the square root of -5 cubed, we need to simplify each expression first. The square root of -3 cubed is the same as (-3)^(3/2), and the square root of -5 cubed is (-5)^(3/2). To simplify these expressions, we need to use the fact that the square root of a number raised to a power is the same as raising the number to half of the power. So, (-3)^(3/2) is the same as taking the cube of -3 and then the square root, which gives us -3 * -3 * -3 = -27, and (-5)^(3/2) is the same as taking the cube of -5 and then the square root, which gives us -5 * -5 * -5 = -125.
Now, we can find the product of these two expressions by multiplying -27 and -125, which equals 3375. Therefore, the product of the square root of -3 cubed and the square root of -5 cubed is 3375.