Final answer:
The volume of the cube with side length 5x²y³ is calculated by cubing the side length, resulting in a volume of 125x⁶y⁹ based on the exponent laws.
Step-by-step explanation:
To determine the volume of a cube with the side length 5x²y³, we apply the formula for the volume of a cube, which is V = s³, where s is the length of a side. Since the side length is given as 5x²y³, cubing this side length gives us:
V = (5x²y³)³
Using the laws of exponents, specifically the cubing of exponentials, we multiply the exponents:
V = 5³ * (x²)³ * (y³)³
V = 125x⁶y⁹
Therefore, the volume of the cube is 125x⁶y⁹, and this is expressed in whatever units of measure are assigned to x and y.