Answer: The answer is 5x³.
Step-by-step explanation: We are given to simplify the following radical expression:
\(R_e=3\sqrt{125x^9}.\)
We are to find the cube root of the 125 and that of x to the power 9 and will multiply both of them to get the complete answer.
The simplification is as follows:
\(R_e\\\\=\sqrt[3]{125x^9}\\\\=\sqrt[3]{5^3(x^3)^3}\\\\=5^{3\times \frac{1}{3}}\times (x^3)^{3\times\frac{1}{3}}\\\\=5\times x^3\\\\=5x^3.\)
Thus, the answer is 5x³.
