Which of the following expressions is equivalent to ${(- x)}^{\frac{1}{5}}$ ?

- \frac{1}{5 x}

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- \frac{1}{x^{5}}

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- \sqrt[5]{x}

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\frac{1}{\sqrt[5]{- x}}

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Solution

The correct option is D $- \sqrt[5]{x}$
The value of $(- x)^{\frac{1}{5}} = (- 1 \times x)^{\frac{1}{5}} = (- 1)^{\frac{1}{5}} . x^{\frac{1}{5}} = - 1 \times \sqrt[5]{x} = - \sqrt[5]{x}$
Hence, the correct option is $C$ .

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