Final answer:
For a cube with side lengths of 1/5 b^3, the volume is (1/5 b^3)^3, resulting in 1/125 b^9. However, this expression for a side length is atypical, and it is possible there might be a typo. Generally, for a cube with a side length of 'b', the volume would be V = b^3.
Step-by-step explanation:
To find the volume of a cube with side lengths expressed as a variable, you simply raise the side length to the third power. In this case, the given side length is 1/5 b^3.
Therefore, the volume of the cube is calculated by raising 1/5 b^3 to the third power:
V = (1/5 b^3)^3
However, it seems there might be a misunderstanding or a typo in the provided expression. Typically, the side length of a cube is a linear measure (e.g., b, 2b, etc.), not a cubic measure (e.g., b^3). So if we assume the side length is 'b' instead, the volume of the cube would be V = b^3. If the side is indeed (1/5 b^3), then the volume is calculated as ((1/5 b^3)^3), which gives V = 1/125 b^9. However, this does not seem to be a standard problem, so please clarify the side length for accurate calculation.