Simplify. \[ \left(\frac{5 a^{4}}{b}\right)^{3} \] Write your answer without parentheses.

To simplify \(\left(\frac{5 a^{4}}{b}\right)^{3}\), we apply the power of a quotient rule, which states that \((\frac{x}{y})^{n} = \frac{x^{n}}{y^{n}}\). Thus, we can break it down: \[ \left(\frac{5 a^{4}}{b}\right)^{3} = \frac{(5 a^{4})^{3}}{b^{3}} \] Now, let's simplify the numerator: \((5 a^{4})^{3} = 5^{3} (a^{4})^{3} = 125 a^{12}\) Putting it all together gives us: \[ = \frac{125 a^{12}}{b^{3}} \] So the final answer is: \[ \frac{125 a^{12}}{b^{3}} \]