5. Simplify. \( \begin{array}{ll}\text { a) }\left(x^{4}\right)^{5} & \text { b) }\left(3 x^{2}\right)^{3} \\ \text { c) } 4(57 a b)^{0} & \text { d) }\left(\frac{y^{11}}{y^{3}}\right)^{2}\end{array} \)

For part a, you can simplify \((x^{4})^{5}\) by using the power of a power rule, which states that \((a^{m})^{n} = a^{m \cdot n}\). Therefore, \((x^{4})^{5} = x^{20}\). In part b, \((3x^{2})^{3}\) can be simplified by distributing the exponent to both the constant and the variable. So you get \((3^{3})(x^{2})^{3} = 27x^{6}\). For part c, \(4(57ab)^{0}\) can be simplified using the property that anything raised to the zero power (except zero itself) equals one. This means \((57ab)^{0} = 1\), thus \(4(1) = 4\). In part d, \(\left(\frac{y^{11}}{y^{3}}\right)^{2}\) simplifies to \(\left(y^{11 - 3}\right)^{2} = \left(y^{8}\right)^{2} = y^{16}\).