Final answer:
To determine the volume of a cube with side length 5x²y³, you cube the side length, resulting in 125x⁶y⁹, which is answer A.
Step-by-step explanation:
The question asks us to determine the volume of a cube with a side length of 5x²y³ using the exponent laws. To find the volume of a cube, we cube the side length. In this case:
V = (5x²y³)³
Applying the cubing of exponentials, we calculate both the numerical and variable parts:
- Cube the numerical coefficient: 5³ = 125
- Multiply the exponents of the variables by 3: (x²)³ = x²× 3 = x⁶ and (y³)³ = y³× 3 = y⁹
Therefore, the volume of the cube is:
V = 125x⁶y⁹
Thus, the correct answer is A. 125x⁶y⁹.