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Which expressions are equivalent to k^(-(1)/(6)) ? Choose all answers that apply: A (1)/(k^(6)) B (k^(-1))^((1)/(6)) c root(6)(k^(-1)) D None of the above

Which expressions are equivalent to k−16 k^{-\frac{1}{6}} ?\newlineChoose all answers that apply:\newlineA 1k6 \frac{1}{k^{6}} \newlineB (k−1)16 \left(k^{-1}\right)^{\frac{1}{6}} \newlinec k−16 \sqrt[6]{k^{-1}} \newlineD None of the above

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Q. Which expressions are equivalent to k−16 k^{-\frac{1}{6}} ?\newlineChoose all answers that apply:\newlineA 1k6 \frac{1}{k^{6}} \newlineB (k−1)16 \left(k^{-1}\right)^{\frac{1}{6}} \newlinec k−16 \sqrt[6]{k^{-1}} \newlineD None of the above
  1. Understand given expression: Understand the given expression.\newlineThe given expression is k−16k^{-\frac{1}{6}}, which means we are looking for expressions that represent the sixth root of 1k\frac{1}{k} or the reciprocal of the sixth power of kk.
  2. Analyze option A: Analyze option A.\newlineOption A is (1)/(k6)(1)/(k^{6}). This is not equivalent to k−(1)/(6)k^{-(1)/(6)} because it represents the reciprocal of kk raised to the sixth power, not the sixth root of 1/k1/k.
  3. Analyze option B: Analyze option B.\newlineOption B is (k−1)16(k^{-1})^{\frac{1}{6}}. This expression represents the sixth root of kk raised to the negative first power, which is equivalent to the sixth root of 1k\frac{1}{k}. Therefore, option B is equivalent to k−16k^{-\frac{1}{6}}.
  4. Analyze option C: Analyze option C.\newlineOption C is k−16\sqrt[6]{k^{-1}}. This expression represents the sixth root of kk raised to the negative first power, which is equivalent to the sixth root of 1k\frac{1}{k}. Therefore, option C is equivalent to k−(16)k^{-\left(\frac{1}{6}\right)}.
  5. Analyze option D: Analyze option D.\newlineOption D states ＂None of the above,＂ which is incorrect because we have found that options B and C are equivalent to k−16k^{-\frac{1}{6}}.

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