Final answer:
The volume of the rectangular prism is represented by the simplified expression 15w^3 + 30w^2, where w represents the width of the prism.
Step-by-step explanation:
To find the volume of a rectangular prism, we use the formula volume = length x width x height. In this case, the length is given as 5 times the width, and the height is described as 6 units more than triple its width. If we let the width be represented by w, then the length becomes 5w, and the height becomes 3w + 6.
The volume can thus be represented by multiplying these terms:
Volume (V) = length x width x height
= 5w x w x (3w + 6).
Simplifying this expression, we get:
V = 5w2 x (3w + 6)
V = 15w3 + 30w2.
This is the simplified expression for the volume of the prism in terms of its width.