\(16\cdot2^9=2^4\cdot2^9=2^{13}\\ 243:3^4=3^5:3^4=3\\ 12^2\cdot2\cdot12^3\cdot6=12^5\cdot12=12^6\\ 16\cdot32=2^4\cdot2^5=2^9\\ 10^9:10000=10^9:10^4=10^5\\ 6^3\cdot2\cdot6^4\cdot3=6^7\cdot6=6^8\)

\(a,3^4.3^5=3^{4+5}=3^9\\ b,12^8:12=12^{8-1}=12^7\\ c,4.8^6.2.8^3=\left(4.2\right).\left(8^6.8^3\right)=8.8^{6+3}=8.8^9=8^{1+9}=8^{10}\)

\(a.3^4.3^5=3^9\)

\(b.12^8:12=12^7\)

\(c.4.8^6.2.8^3\)

\(=\left(4.2\right)8^6.8^3\)

\(=8.8^6.8^3=8^{10}\)

Lời giải:
\(\frac{4.3^9+8.(-3)^7}{(-3)^{10}+20.(-3)^7}=\frac{4.3^9-8.3^7}{3^{10}-20.3^7}=\frac{3^7(4.3^2-8)}{3^7(3^3-20)}\\ =\frac{3^7.28}{3^7.7}=\frac{28}{7}=4\)

Lời giải:
\(\frac{4.3^9+8.(-3)^7}{(-3)^{10}+20.(-3)^7}=\frac{4.3^9-8.3^7}{3^{10}-20.3^7}=\frac{3^7(4.3^2-8)}{3^7(3^3-20)}\\ =\frac{3^7.28}{3^7.7}=\frac{28}{7}=4\)

c: \(C=\dfrac{\left(\dfrac{2}{5}\cdot5\right)^7+\dfrac{9^3}{4^3}:\dfrac{3^3}{16^3}}{2^7\cdot5^2+2^9}=\dfrac{1+1728}{3712}=\dfrac{1729}{3712}\)

\(D=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}=\dfrac{3^5-3^4}{3^6+3^5}=\dfrac{3^4\left(3-1\right)}{3^5\left(3+1\right)}=\dfrac{2}{3\cdot4}=\dfrac{2}{12}=\dfrac{1}{6}\)

\(E=\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}=\dfrac{5^{10}\cdot7^3\cdot\left(-6\right)}{5^9\cdot7^3\cdot9}=5\cdot\dfrac{-2}{3}=\dfrac{-10}{3}\)

\(\frac{2^{12}.3^5-4^6.3^6}{2^{12}.9^3+8^4.3^5}\)

\(=\frac{2^{12}.3^5-4^6.3.3^5}{2^{12}.3.3^5+4^6.3^5}\)

\(=\frac{1-3}{3+1}\)

\(=\frac{-1}{2}\)

P=2¹².3⁵-4⁶.3⁶/2¹².9³+8⁴.3⁵

P=2¹².3⁵-(2²)⁶.3⁶/2¹².(3³)³+(2³)⁴.3⁵

P=2¹².3⁵-2¹².3⁶/2¹².3⁹+2¹².3⁵

P=2¹².(3⁵-3⁶)/2¹².(3⁹+3⁵)

P=3⁵-3⁶/3⁹+3⁵