If x^{m}=\sqrt{x\sqrt{x\sqrt{x}}}, then what is the value of m?
- A. \frac{1}{8} ✓
- B. \frac{1}{4}
- C. \frac{3}{4}
- D. \frac{7}{4}
Correct Answer: A. \frac{1}{8}
Explanation
Expressing the nested roots as fractional powers: x\sqrt{x\sqrt{x}} = x \times x^{1/2} \times x^{1/4} = x^{1 + 1/2 + 1/4} = x^{7/4}. Taking the 14th root yields (x^{7/4})^{1/14} = x^{7/56} = x^{1/8}. Hence, m = \frac{1}{8}.
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