We are given an artifact with the width of the base w inches.
We know that the artifact is presented in the display case in the shape of a cube. Each side of the cube is 3 times longer than the width of the artifact. The width of the artifact is w inches. This means that the edge of the cube is 3w inches long.
We want to find the power that represents the volume of the display case. Recall the formula for the volume of a cube with an edge length of s.
V = s^3
In our case s=3w. This means that we need to substitute 3w for s into the formula to find the volume of the display case.
In Part A we found the expression for the volume of the display case. Now, we want to simplify it.
V = (3w)^3
The expression ( 3w)^3 is a power of a product. To simplify it, we can use the Power of a Product Property.
Power of a Product Property
To find a power of a product, we can find the power of each factor and multiply.
Let's apply this property to our expression!
V = (3w)^3 = 3^3 * w^3
The expression contains two powers and one of them is a power of a number. We can find its value to simplify the expression completely.
