Simplify: ((a^2)/(b^5))^4 (a^8)/(b^9) (a^6)/(b^9) (a^8)/(b^20) (a^8)/(b^20)

To simplify the expression \(\left(\frac{a^{2}}{b^{5}}\right)^{4}\), we need to apply the power of a quotient rule, which states that \(\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}\).<br /><br />Given:<br />\[<br />\left(\frac{a^{2}}{b^{5}}\right)^{4}<br />\]<br /><br />We can rewrite this as:<br />\[<br />\frac{(a^{2})^{4}}{(b^{5})^{4}}<br />\]<br /><br />Next, we apply the power rule for exponents, which states that \((x^m)^n = x^{m \cdot n}\):<br /><br />\[<br />(a^{2})^{4} = a^{2 \cdot 4} = a^{8}<br />\]<br />\[<br />(b^{5})^{4} = b^{5 \cdot 4} = b^{20}<br />\]<br /><br />So, the expression simplifies to:<br />\[<br />\frac{a^{8}}{b^{20}}<br />\]<br /><br />Therefore, the correct answer is:<br />\[<br />\frac{a^{8}}{b^{20}}<br />\]