Final answer:
The 5th root of 243x^10 y^5 z^10 can be found by calculating the 5th root of each part separately, resulting in 3x^2 y z^2
Step-by-step explanation:
To find the 5th root of 243x^10 y^5 z^10, one can break down the mathematics as follows:
- Firstly, determine the 5th root of 243, which is 3.
- Secondly, the 5th root of 'x' to the power of 10 (x^10) is x^2 (since 10 divided by 5 is 2).
- Thirdly, the 5th root of 'y' to the power of 5 (y^5) is y (since 5 divided by 5 is 1).
- Lastly, the 5th root of 'z' to the power of 10 (z^10) is z^2 (once again, 10 divided by 5 is 2).
This provides the final answer of 3x^2 y z^2. This method could be applied to any problem where the task is to find a root of an expression including variables raised to power.
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