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Use radical notation to write the expression. Simplify if possible. Assume that all variables represent positive real numbers. \[ \begin{array}{l}(5 x+3)^{\frac{3}{4}} \\ \text { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { A. }(5 x+3)^{\frac{3}{4}}=\square \\ (\text { Simplify your answer. Type an exact answer, using radicals as needed.) } \\ \text { B. The answer is not a real number. }\end{array} \]

Ask by Pritchard Joseph. in the United States
Mar 15,2025

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\[ (5x + 3)^{\frac{3}{4}} = \sqrt[4]{(5x + 3)^3} \]

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To express \( (5x + 3)^{\frac{3}{4}} \) using radical notation, we can rewrite it as: \[ (5x + 3)^{\frac{3}{4}} = \sqrt[4]{(5x + 3)^3} \] This expresses the problem in radical form, where we have the fourth root of \((5x + 3)^3\). To simplify, we won't simplify this expression further since \( (5x + 3)^3 \) does not have any common factors that would allow for further reduction when taking the fourth root. Thus the answer in radical notation is: \[ \sqrt[4]{(5x + 3)^3} \]

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