erform the operation and simplify the answer fully. \[ \frac{2}{7 x^{3}} \div \frac{2}{3 x^{3}} \]

To perform the operation, you can multiply by the reciprocal of the second fraction: \[ \frac{2}{7 x^{3}} \div \frac{2}{3 x^{3}} = \frac{2}{7 x^{3}} \times \frac{3 x^{3}}{2} \] Now, you can simplify by canceling out the \(2\) in the numerator and denominator: \[ = \frac{3}{7} \cdots (x^{3} \text{ cancels out}) \] Thus, the simplified answer is: \[ \frac{3}{7} \]