a: \(=2^2\cdot9\cdot\dfrac{1}{6\cdot9}\cdot\dfrac{4^2}{9^2}=\dfrac{2^2}{6}\cdot\dfrac{2^4}{3^4}=\dfrac{2^6}{2\cdot3\cdot3^4}=\dfrac{2^5}{3^5}=\left(\dfrac{2}{3}\right)^5\)

b: \(=2^8\cdot\dfrac{3^4}{2^4}=3^4\cdot2^4=6^4\)

c: \(=\dfrac{\left(\dfrac{1}{2}\right)^3\cdot2^3\cdot\left(\dfrac{1}{2}\right)^2}{\left(-8\right)^2\cdot16}\cdot2^6=\dfrac{\dfrac{1}{2^2}}{64\cdot16}\cdot64=\dfrac{1}{4}:16=\dfrac{1}{64}=\left(\dfrac{1}{8}\right)^2\)

a: \(=2^2\cdot9\cdot\dfrac{1}{3^3\cdot2}\cdot\dfrac{2^4}{3^4}=\dfrac{2^4\cdot2^2}{2}\cdot\dfrac{9}{3^3\cdot3^4}=\dfrac{2^5}{3^5}=\left(\dfrac{2}{3}\right)^5\)

b: \(=2^8\cdot\dfrac{3^4}{2^4}=3^4\cdot2^4=6^4\)

c: \(=\dfrac{\dfrac{1}{2^3}\cdot\dfrac{1}{2^2}\cdot8}{\left(-8\right)^2\cdot2^4}\cdot2^6=\dfrac{1}{2^2}\cdot2^6:2^{10}=\dfrac{2^4}{2^{10}}=\dfrac{1}{2^6}=\left(\dfrac{1}{8}\right)^2\)

a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)

b: \(=\left(\dfrac{3}{7}\cdot\dfrac{5}{3}\right)^6\cdot\dfrac{5}{3}\cdot\dfrac{3}{7}:\left(\dfrac{7^3}{5^4}\right)^{-2}\)

\(=\left(\dfrac{5}{7}\right)^6\cdot\dfrac{5}{7}\cdot\left(\dfrac{5}{7}\right)^6\cdot5^2\)

\(=\left(\dfrac{5}{7}\right)^{13}\cdot5^2\)

c: \(=5^4\cdot2.5^{-5}\cdot125\cdot0.04\)

\(=5^4\cdot5\cdot\left(\dfrac{5}{2}\right)^{-5}\)

\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)

a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)

b: \(=\left(\dfrac{3}{7}\right)^5\cdot\left(\dfrac{3}{7}\right)\cdot\dfrac{5^6}{3^6}:\left(\dfrac{625}{343}\right)^2\)

\(=\dfrac{3^6}{7^6}\cdot\dfrac{5^6}{3^6}:\dfrac{5^8}{7^6}\)

\(=\dfrac{1}{5^2}\)

c: \(=5^{4+3}\cdot\left(\dfrac{5}{2}\right)^{-5}\cdot\dfrac{1}{25}\)

\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)

a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)

b: \(=\left(\dfrac{3}{7}\right)^5\cdot\left(\dfrac{3}{7}\right)\cdot\dfrac{5^6}{3^6}:\left(\dfrac{625}{343}\right)^2\)

\(=\dfrac{3^6}{7^6}\cdot\dfrac{5^6}{3^6}:\dfrac{5^8}{7^6}\)

\(=\dfrac{1}{5^2}\)

c: \(=5^{4+3}\cdot\left(\dfrac{5}{2}\right)^{-5}\cdot\dfrac{1}{25}\)

\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)

a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)

b: \(=\left(\dfrac{3}{7}\right)^5\cdot\left(\dfrac{3}{7}\right)\cdot\dfrac{5^6}{3^6}:\left(\dfrac{625}{343}\right)^2\)

\(=\dfrac{3^6}{7^6}\cdot\dfrac{5^6}{3^6}:\dfrac{5^8}{7^6}\)

\(=\dfrac{1}{5^2}\)

c: \(=5^{4+3}\cdot\left(\dfrac{5}{2}\right)^{-5}\cdot\dfrac{1}{25}\)

\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)

a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)

b: \(=\left(\dfrac{3}{7}\right)^5\cdot\left(\dfrac{3}{7}\right)\cdot\dfrac{5^6}{3^6}:\left(\dfrac{625}{343}\right)^2\)

\(=\dfrac{3^6}{7^6}\cdot\dfrac{5^6}{3^6}:\dfrac{5^8}{7^6}\)

\(=\dfrac{1}{5^2}\)

c: \(=5^{4+3}\cdot\left(\dfrac{5}{2}\right)^{-5}\cdot\dfrac{1}{25}\)

\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)

D,       Vì 3^2=9 và -3^2=9 còn 5^2=25

D

a)\({\left[ {{{\left( { - \frac{1}{6}} \right)}^3}} \right]^4}\) (với \(a =  - \frac{1}{6}\))

\(=(- \frac{1}{6})^{3. 4}=(- \frac{1}{6})^{12}\)

b)\({\left[ {{{\left( { - 0,2} \right)}^4}} \right]^5}\) (với \(a =  - 0,2\))

\(=(-0,2)^{4.5}=(-0,2)^{20}\)