Simplify Radical Expression

In this problem, we are asked to simplify the product of two radical expressions. Let's write them down first.

Because we are multiplying these two terms together, we can use the associative and commutative properties of multiplication to group the constants and the radicals.

First, let's multiply the coefficients five and negative three to get negative fifteen.

Next, we apply the product property of radicals, which states that the product of two fourth roots is equal to the fourth root of their products.

Now we can combine the terms inside the radical. Six times twenty seven gives us one hundred and sixty two, and x times x cubed is x to the fourth power.

To simplify further, we should check if one hundred and sixty two has any factors that are perfect fourth powers.