1. **State the problem:** Solve the equation $$x^{5} - 9x^{5} + 14 = 0$$. 2. **Simplify the equation:** Combine like terms: $$x^{5} - 9x^{5} = -8x^{5}$$ So the equation becomes: $$-8x^{5} + 14 = 0$$ 3. **Isolate the term with $x$:** $$-8x^{5} = -14$$ Divide both sides by $-8$: $$x^{5} = \frac{14}{8} = \frac{7}{4}$$ 4. **Solve for $x$:** Take the fifth root of both sides: $$x = \left(\frac{7}{4}\right)^{\frac{1}{5}}$$ 5. **Explain the fifth root:** The fifth root means the number which, when raised to the power 5, gives $\frac{7}{4}$. This is the exact solution. 6. **Regarding $(3/5)^5$ in your question:** If you meant to evaluate $(\frac{3}{5})^{5}$, it is simply: $$\left(\frac{3}{5}\right)^5 = \frac{3^5}{5^5} = \frac{243}{3125}$$ This is unrelated to the original equation but is a straightforward exponentiation. **Final answer:** $$x = \left(\frac{7}{4}\right)^{\frac{1}{5}}$$