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Which expressions are equivalent to (root(4)(x))^(-1) ? Choose all answers that apply: A x^(-4) B (sqrtx)^(-4) c -root(4)(x) D None of the above

Which expressions are equivalent to (x4)−1 (\sqrt[4]{x})^{-1} ?\newlineChoose all answers that apply:\newlineA x−4 x^{-4} \newlineB (x)−4 (\sqrt{x})^{-4} \newlinec −x4 -\sqrt[4]{x} \newlineD None of the above

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Identify equivalent linear expressions Iright chevron icon

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Q. Which expressions are equivalent to (x4)−1 (\sqrt[4]{x})^{-1} ?\newlineChoose all answers that apply:\newlineA x−4 x^{-4} \newlineB (x)−4 (\sqrt{x})^{-4} \newlinec −x4 -\sqrt[4]{x} \newlineD None of the above
  1. Step 11: Understand the expression: Understand the expression (x4)−1(\sqrt[4]{x})^{-1}. The expression represents the fourth root of xx, raised to the power of −1-1. This means we are looking for the reciprocal of the fourth root of xx.
  2. Step 22: Simplify the expression: Simplify the expression using the properties of exponents.\newlineThe reciprocal of a number is the same as raising that number to the power of −1-1. Therefore, (x4)−1(\sqrt[4]{x})^{-1} is the same as x−14x^{-\frac{1}{4}}.
  3. Step 33: Compare with given choices: Compare the simplified expression with the given choices.\newlineA. x(−4)x^{(-4)} is not equivalent because it represents xx raised to the power of −4-4, not −14-\frac{1}{4}.\newlineB. (x)(−4)(\sqrt{x})^{(-4)} is not equivalent because it represents the square root of xx raised to the power of −4-4, which is x(−2)x^{(-2)}, not x(−14)x^{(-\frac{1}{4})}.\newlineC. −x4-\sqrt[4]{x} is not equivalent because it represents the negative fourth root of xx, not the reciprocal of the fourth root of xx.\newlineD. None of the above is the correct choice because none of the given options match x(−14)x^{(-\frac{1}{4})}.

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