\(4A\\ a,\left(\dfrac{1}{9}\right)^6.\left(\dfrac{1}{3}\right)^3=\left[\left(\dfrac{1}{3}\right)^2\right]^6.\left(\dfrac{1}{3}\right)^3=\left(\dfrac{1}{3}\right)^{12}.\left(\dfrac{1}{3}\right)^3=\left(\dfrac{1}{3}\right)^{15}\\ b,\left(-\dfrac{2}{3}\right)^2.\left(\dfrac{9}{4}\right)^2=\left(-\dfrac{2}{3}\right)^2.\left[\left(-\dfrac{2}{3}\right)^2\right]^2=\left(\dfrac{2}{3}\right)^2.\left(\dfrac{2}{3}\right)^4=\left(\dfrac{2}{3}\right)^6\\ c,\left(\dfrac{7}{3}\right)^3:\left(-\dfrac{35}{9}\right)^3=\left(\dfrac{7}{3}.\dfrac{-9}{35}\right)^3=\left(-\dfrac{3}{5}\right)^3\)
\(5A\\ a,125.5^2.\dfrac{1}{625}.5^3=5^3.5^2.5^3.\dfrac{1}{5^4}=5^{3+2+3-4}=5^4\\ b,8.32:\left(2^4.\dfrac{1}{32}\right)=2^3.2^5.\left(2^4.\dfrac{1}{2^5}\right)=2^{3+5+4-5}=2^7\\ c,6^3.5^2.\left(\dfrac{5}{6}\right)^3=6^3.5^2.\dfrac{5^3}{6^3}=\dfrac{6^3}{6^3}.5^2.5^3=5^{2+3}=5^5\)
\(5B\\ a,2401.\left(\dfrac{1}{7}\right)^2.\dfrac{1}{7}.49^2=7^4.\left(\dfrac{1}{7}\right)^{2+1}.\left(7^2\right)^2=7^4.\left(\dfrac{1}{7}\right)^3.7^4=\dfrac{7^4.7^4}{7^3}=7^{4+4-3}=7^5\)
\(b,9.81.\left(3^5.\dfrac{1}{27}\right)=3^2.3^4.\left(3^5.\dfrac{1}{3^3}\right)=\dfrac{3^2.3^4.3^5}{3^3}=3^{2+4+5-3}=3^8\\ c,3^4.7^2.\left(-\dfrac{7}{3}\right)^4=3^4.7^2.\left(\dfrac{7}{3}\right)^4=\dfrac{3^4}{3^4}.7^2.7^4=1.7^6=7^6\)
\(4B\\ a,\left(\dfrac{2}{3}\right)^6.\left(\dfrac{8}{27}\right)^2=\left(\dfrac{2}{3}\right)^6.\left[\left(\dfrac{2}{3}\right)^3\right]^2=\left(\dfrac{2}{3}\right)^6.\left(\dfrac{2}{3}\right)^6=\left(\dfrac{2}{3}\right)^{6+6}=\left(\dfrac{2}{3}\right)^{12}\\ b,\left(\dfrac{3}{5}\right)^2.\left(-\dfrac{9}{25}\right)^2=\left(\dfrac{3}{5}\right)^2.\left(\dfrac{9}{25}\right)^2=\left(\dfrac{3}{5}\right)^2.\left[\left(\dfrac{3}{5}\right)^2\right]^2\\ =\left(\dfrac{3}{5}\right)^2.\left(\dfrac{3}{5}\right)^4=\left(\dfrac{3}{5}\right)^{2+4}=\left(\dfrac{3}{5}\right)^6\\ c,\left(-\dfrac{5}{2}\right)^3.\left(-\dfrac{8}{125}\right)^3=\left(-\dfrac{5}{3}\right)^3.\left(-\dfrac{2}{5}\right)^3=\left[\dfrac{-5.\left(-2\right)}{3.5}\right]^3=\left(\dfrac{2}{3}\right)^3\)
