a)\(\frac{243}{22}\)

b)\(\frac{4}{5}=0,8\)

Giúp mình với

\(10.\frac{\left(2^2\right)^6.\left(3^3\right)^5+\left(2.3\right)^9.\left(2^3.3.5\right)}{\left(2^4\right)^3.3^{12}-\left(2.3\right)^{11}}\)

\(=10.\frac{2^{12}.3^{15}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=10.\frac{2^{12}.3^{10}\left(3^5+1.5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)

\(=10\frac{2\left(3^5+5\right)}{3.5}\)

\(=10.\frac{496}{15}\)

\(=\frac{992}{3}\)

Study well 

10.\(\frac{241864704+1209323520}{2176782336-6^{11}}\)

=10.\(\frac{362797224}{1813985280}\)

=2,000000926

\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1+5\right)}{6^{12}-6^{11}}=\frac{2^{12}.3^{10}.6}{6^{11}.\left(6-1\right)}=\frac{2^{12}.3^{10}.2.3}{6^{11}.\left(6-1\right)}=\frac{2^{13}.3^{11}}{6^{11}.5}=\frac{2^{11}.3^{11}.2^2}{6^{11}.5}=\frac{6^{11}.4}{6^{11}.5}=\frac{4}{5}\)

Bài2

a) ta có : 10^19 + 10^18 +10^17 = 10^17 (10^2+10+1)

                                               = 10^17 . 111

Do 10 chia hết cho 5 nên 10^17 cũng chia hết cho 5. Mà 10^17 cũng chia hết cho 111 

nên 10^17 chia hết cho 111x5 = 555 ( vì (111;5)=1)

Vậy 10^19 + 10^18 + 10^17 chia hết cho 555

b) Ta có : 7+7^2+7^3+7^4+...+7^84

              = (7+7^2+7^3)+(7^4+7^5+7^6)+...+(7^82+7^83+7^84)

              = 7(1+7+7^2) + 7^4(1+7+7^2)+...+7^82(1+7+7^2)

              = 7.57           +  7^4.57        +...+   7^82.57

               = 57(7.7^4....7^82) chia hết cho 57

Vậy 7+7^2+7^3+...+7^84 chia hết cho 57