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\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3^2}{7^2}\right)^6=\left(\frac{3}{7}\right)^{21}:\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^{21-12}=\left(\frac{3}{7}\right)^9\)
\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left(\left(\frac{3}{7}\right)^2\right)^6\)
\(=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}\)
\(=\left(\frac{3}{7}\right)^{21-12}\)
\(=\left(\frac{3}{7}\right)^9\)
\(\left(\frac{3}{7}\right)^{21}.\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}.\left(\frac{3^2}{7^2}\right)^6=\left(\frac{3}{7}\right)^{21}.\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^{33}\)
\(D=\left(\frac{3}{7}\right)^{21}:\left(\left(\frac{3}{7}\right)^2\right)^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{2.6}=\left(\frac{3}{7}\right)^9\)
\(E=\left(-\frac{1}{3}\right)^{7+9}:\left(-\frac{1}{3}\right)^{5.3}+\left(-2\right)^{12+3}:\left(-2\right)^{15}=\left(-\frac{1}{3}\right)^{16}:\left(-\frac{1}{3}\right)^{15}+\left(-2\right)^{15}:\left(-2\right)^{15}=-\frac{1}{3}+1=\frac{2}{3}\)
\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3^2}{7^2}\right)^6=\left(\frac{3}{7}\right)^{21}:\left[\left(\frac{3}{7}\right)^2\right]^6\)
\(=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^{21-12}=\left(\frac{3}{7}\right)^9\)
\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^{10}=\frac{3^{21}}{7^{21}}:\frac{9^{10}}{49^{10}}=\frac{3^{21}}{7^{21}}:\frac{\left(3^2\right)^{10}}{\left(7^2\right)^{10}}=\frac{3^{21}}{7^{21}}:\frac{3^{20}}{7^{20}}=\frac{3^{21}}{7^{21}}.\frac{7^{20}}{3^{20}}=\frac{3}{7}\)