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

Simplify the expression by following steps: - step0: Solution: \(\left(x^{4}\right)^{5}\) - step1: Multiply the exponents: \(x^{4\times 5}\) - step2: Multiply the numbers: \(x^{20}\) Calculate or simplify the expression \( (3 x^{2})^{3} \). Simplify the expression by following steps: - step0: Solution: \(\left(3x^{2}\right)^{3}\) - step1: Use the properties of exponents: \(3^{3}\left(x^{2}\right)^{3}\) - step2: Evaluate the power: \(27x^{6}\) Calculate or simplify the expression \( (y^{11}/y^{3})^{2} \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{y^{11}}{y^{3}}\right)^{2}\) - step1: Divide the terms: \(\left(y^{8}\right)^{2}\) - step2: Transform the expression: \(y^{8\times 2}\) - step3: Multiply the numbers: \(y^{16}\) Calculate or simplify the expression \( 4(57 a b)^{0} \). Simplify the expression by following steps: - step0: Solution: \(4\left(57ab\right)^{0}\) - step1: Rewrite the expression: \(4\times 1\) - step2: Multiply: \(4\) Here are the simplified results for each part: a) \( \left(x^{4}\right)^{5} = x^{20} \) b) \( \left(3 x^{2}\right)^{3} = 27x^{6} \) c) \( 4(57 a b)^{0} = 4 \) (since any non-zero number raised to the power of 0 is 1) d) \( \left(\frac{y^{11}}{y^{3}}\right)^{2} = y^{16} \) So the final simplified expressions are: - a) \( x^{20} \) - b) \( 27x^{6} \) - c) \( 4 \) - d) \( y^{16} \)