What is the simplified form of the following expression? Assume x≠0. ^5√10x/3x^3.
2 answers:
To solve this problem you must apply the proccedure shown below:
1. You have the following expression given in the problem above:
![\sqrt[5]{10x/3x^3} ](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B10x%2F3x%5E3%7D%20%0A)
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2. You can rewrite the expression as following:
</span>![(\sqrt[5]{10}) x^{1/5}/ (\sqrt[5]{3}) x^{3/5}](https://tex.z-dn.net/?f=%20%28%5Csqrt%5B5%5D%7B10%7D%29%20x%5E%7B1%2F5%7D%2F%20%28%5Csqrt%5B5%5D%7B3%7D%29%20x%5E%7B3%2F5%7D%20)
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3. Applying the exponetns properties, you can substract the exponents whose bases are equal. In this case, you need to substract the exponents of x:
</span>![\sqrt[5]{10}/ (\sqrt[5]{3})x^{2/5} ](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B10%7D%2F%20%28%5Csqrt%5B5%5D%7B3%7D%29x%5E%7B2%2F5%7D%0A)
![\sqrt[5]{10/3 x^{2}}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B10%2F3%20x%5E%7B2%7D%7D)
Therefore, the answer is:![\sqrt[5]{10/3x^{2} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B10%2F3x%5E%7B2%7D%20%7D%20)
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1. You have the following expression given in the problem above:
2. You can rewrite the expression as following:
</span>
3. Applying the exponetns properties, you can substract the exponents whose bases are equal. In this case, you need to substract the exponents of x:
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Therefore, the answer is:
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