Simplify. ((-5b^2)/(a))^3 Write your an ewer without

To simplify the expression \((\frac{-5b^2}{a})^3\), we need to apply the power of a quotient rule and the power of a product rule.<br /><br />The power of a quotient rule states that \(\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}\).<br /><br />The power of a product rule states that \((xy)^n = x^n y^n\).<br /><br />Let's apply these rules step by step:<br /><br />1. Apply the power of a quotient rule:<br /> \[<br /> \left(\frac{-5b^2}{a}\right)^3 = \frac{(-5b^2)^3}{a^3}<br /> \]<br /><br />2. Apply the power of a product rule to the numerator:<br /> \[<br /> (-5b^2)^3 = (-5)^3 (b^2)^3<br /> \]<br /><br />3. Calculate the powers:<br /> \[<br /> (-5)^3 = -125<br /> \]<br /> \[<br /> (b^2)^3 = b^{2 \cdot 3} = b^6<br /> \]<br /><br />4. Combine the results:<br /> \[<br /> (-5b^2)^3 = -125b^6<br /> \]<br /><br />5. Substitute back into the fraction:<br /> \[<br /> \frac{(-5b^2)^3}{a^3} = \frac{-125b^6}{a^3}<br /> \]<br /><br />So, the simplified form of the expression \((\frac{-5b^2}{a})^3\) is:<br />\[<br />\boxed{\frac{-125b^6}{a^3}}<br />\]