Final answer:
To find the cube root of 1/9x^2y, break it down into three parts: 1/3 for 1/9, x^(2/3) for x^2, and y^(1/3) for y. Combine them to get the cube root answer.
Step-by-step explanation:
To find the cube root of 1/9x^2y, we can break it down:
- First, find the cube root of 1/9. The cube root of a number is the number that, when raised to the power of 3, equals the original number. In this case, the cube root of 1/9 is 1/3.
- Next, find the cube root of x^2. The cube root of a variable raised to a power is equal to the variable raised to the power divided by 3. In this case, the cube root of x^2 is x^(2/3).
- Finally, find the cube root of y. Since y is already to the power of 1, the cube root of y is y^(1/3).
Therefore, the cube root of 1/9x^2y is (1/3)x^(2/3)y^(1/3).