In Exercises 25 and 26, simplify the expression. Write your answer using only positive exponents. 25. \( \left(\frac{5 x^{-4} y^{3}}{2 x^{2} y^{0}}\right)^{2} \cdot\left(\frac{4 x y}{y^{3}}\right)^{2} \) 26. \( \left(\frac{2 a^{0} b^{-4}}{b^{3}}\right)^{4} \cdot\left(\frac{a^{3} b^{-2}}{3 b^{4} a^{-4}}\right)^{3} \)

Calculate or simplify the expression \( \left(\frac{5 x^{-4} y^{3}}{2 x^{2} y^{0}}\right)^{2} \cdot\left(\frac{4 x y}{y^{3}}\right)^{2} \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{5x^{-4}y^{3}}{2x^{2}y^{0}}\right)^{2}\left(\frac{4xy}{y^{3}}\right)^{2}\) - step1: Multiply by \(a^{-n}:\) \(\left(\frac{5x^{-4}y^{3}x^{-2}y^{0}}{2}\right)^{2}\left(\frac{4xy}{y^{3}}\right)^{2}\) - step2: Evaluate the power: \(\left(\frac{5x^{-4}y^{3}x^{-2}\times 1}{2}\right)^{2}\left(\frac{4xy}{y^{3}}\right)^{2}\) - step3: Multiply the terms: \(\left(\frac{5x^{-6}y^{3}}{2}\right)^{2}\left(\frac{4xy}{y^{3}}\right)^{2}\) - step4: Rewrite the expression: \(\left(\frac{5y^{3}}{2x^{6}}\right)^{2}\left(\frac{4xy}{y^{3}}\right)^{2}\) - step5: Divide the terms: \(\left(\frac{5y^{3}}{2x^{6}}\right)^{2}\left(\frac{4x}{y^{2}}\right)^{2}\) - step6: Rewrite the expression: \(\frac{25y^{6}}{4x^{12}}\times \frac{16x^{2}}{y^{4}}\) - step7: Reduce the numbers: \(\frac{25y^{2}}{4x^{12}}\times 16x^{2}\) - step8: Reduce the fraction: \(\frac{25y^{2}}{x^{10}}\times 4\) - step9: Multiply the terms: \(\frac{25y^{2}\times 4}{x^{10}}\) - step10: Multiply the terms: \(\frac{100y^{2}}{x^{10}}\) Calculate or simplify the expression \( \left(\frac{2 a^{0} b^{-4}}{b^{3}}\right)^{4} \cdot\left(\frac{a^{3} b^{-2}}{3 b^{4} a^{-4}}\right)^{3} \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{2a^{0}b^{-4}}{b^{3}}\right)^{4}\left(\frac{a^{3}b^{-2}}{3b^{4}a^{-4}}\right)^{3}\) - step1: Multiply by \(a^{-n}:\) \(\left(\frac{2a^{0}b^{-4}}{b^{3}}\right)^{4}\left(\frac{a^{3}b^{-2}a^{4}b^{-4}}{3}\right)^{3}\) - step2: Evaluate the power: \(\left(\frac{2\times 1\times b^{-4}}{b^{3}}\right)^{4}\left(\frac{a^{3}b^{-2}a^{4}b^{-4}}{3}\right)^{3}\) - step3: Reduce the fraction: \(\left(\frac{2}{b^{7}}\right)^{4}\left(\frac{a^{3}b^{-2}a^{4}b^{-4}}{3}\right)^{3}\) - step4: Multiply: \(\left(\frac{2}{b^{7}}\right)^{4}\left(\frac{a^{7}b^{-6}}{3}\right)^{3}\) - step5: Rewrite the expression: \(\left(\frac{2}{b^{7}}\right)^{4}\left(\frac{a^{7}}{3b^{6}}\right)^{3}\) - step6: Evaluate the power: \(\frac{16}{b^{28}}\times \left(\frac{a^{7}}{3b^{6}}\right)^{3}\) - step7: Evaluate the power: \(\frac{16}{b^{28}}\times \frac{a^{21}}{27b^{18}}\) - step8: Multiply the terms: \(\frac{16a^{21}}{b^{28}\times 27b^{18}}\) - step9: Multiply the terms: \(\frac{16a^{21}}{27b^{46}}\) The simplified expression for Exercise 25 is \( \frac{100y^{2}}{x^{10}} \) and for Exercise 26 is \( \frac{16a^{21}}{27b^{46}} \).