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

To write the expression \( (5x)^{\frac{3}{4}} \) in radical notation, we can express the fractional exponent in terms of roots. The expression can be rewritten as: \[ (5x)^{\frac{3}{4}} = \sqrt[4]{(5x)^3} = \sqrt[4]{125x^3} \] So, the answer simplified is \( \sqrt[4]{125x^3} \). This is a perfect opportunity to reflect on how rules of exponents and radicals interact. Remembering the way to move between forms can open up new ways to simplify expressions, especially as problems get more complex! Furthermore, when working with roots, it’s essential to remember that for positive real numbers, the operations hold true. Understanding how to separate coefficients and variables under radical sign will enhance your problem-solving skills and mathematical intuition!