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a: \(=\dfrac{3^6\cdot2^{21}}{5^{18}\cdot7^9\cdot7^3}=\dfrac{3^6\cdot2^{21}}{5^{18}\cdot7^{12}}\)
b: \(=\dfrac{3^{10}\cdot3^7\cdot2^7\cdot2^2}{2^9\cdot5^9\cdot5^8}=\dfrac{3^{17}}{5^{17}}\)
a)\(\frac{6^3+3\cdot6^2+3^3}{-13}=\frac{3^3\cdot2^3+3^3\cdot2^2+3^3}{-13}=\frac{3^3\left(2^3+2^2+1\right)}{-13}=-3^3=-27\)
b) \(\frac{2^3+3\cdot2^6-4^3}{2^3+3^2}=\frac{8+3\cdot64-64}{8+9}=\frac{8+192-64}{17}=\frac{136}{17}=8\)
c) \(\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}=\frac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}=\frac{2^{11}\cdot3^{10}\left(2+2\cdot5\right)}{2^{11}\cdot3^{10}\cdot\left(2\cdot3^2-3\right)}=\frac{12}{18-3}=\frac{12}{15}\)
d) \(\frac{5^5\cdot20^3-5^4\cdot20^3+5^7\cdot4^5}{\left(20+5\right)^3\cdot4^5}=\frac{5^5\cdot20^3-5^4\cdot20^3+20^3\cdot20^2\cdot5^2}{5^6\cdot4^5}=\frac{20^3\left(5^5-5^4+5^4\cdot4^2\right)}{20^5\cdot5}\)\(=\frac{5^4\left(5-1+16\right)}{20^2\cdot5}=\frac{5^4\cdot20}{20^2\cdot5}=\frac{5^3}{20}=\frac{5^3}{5\cdot4}=\frac{25}{4}\)
Bài giải
a)\(\frac{6^3+3\cdot6^2+3^3}{-13}=\frac{3^3\cdot2^3+3^3\cdot2^2+3^3}{-13}=\frac{3^3\left(2^3+2^2+1\right)}{-13}=-3^3=-27\)
b) \(\frac{2^3+3\cdot2^6-4^3}{2^3+3^2}=\frac{8+3\cdot64-64}{8+9}=\frac{8+192-64}{17}=\frac{136}{17}=8\)
c) \(\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}=\frac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}=\frac{2^{11}\cdot3^{10}\left(2+2\cdot5\right)}{2^{11}\cdot3^{10}\cdot\left(2\cdot3^2-3\right)}=\frac{12}{18-3}=\frac{12}{15}\)
d) \(\frac{5^5\cdot20^3-5^4\cdot20^3+5^7\cdot4^5}{\left(20+5\right)^3\cdot4^5}=\frac{5^5\cdot20^3-5^4\cdot20^3+20^3\cdot20^2\cdot5^2}{5^6\cdot4^5}=\frac{20^3\left(5^5-5^4+5^4\cdot4^2\right)}{20^5\cdot5}\)\(=\frac{5^4\left(5-1+16\right)}{20^2\cdot5}=\frac{5^4\cdot20}{20^2\cdot5}=\frac{5^3}{20}=\frac{5^3}{5\cdot4}=\frac{25}{4}\)
\(5^5.20^3-5^4.20^3=20^3\left(5^5-5^4\right)=20^3.5^4\left(5-1\right)=20^3.5^4.4\)
\(5^5.20^3-5^4.20^3+5^7.4^5=5^3.4^3.5^4.4+5^7.4^5=5^7.4^4+5^7.4^5=5^7.4^4\left(1+4\right)=5^8.4^4\)
\(\left(20+5\right)^3.4^5=25^3.4^5=\left(5^2\right)^3.4^5=5^6.4^5\)
Vậy kết quả của biểu thức là: \(\frac{5^8.4^4}{5^6.4^5}=\frac{25.5^6.4^4}{5^6.4^4.4}=\frac{25}{4}\)
\(\frac{5^5.20^3-5^4.20^3+5^7.4^5}{\left(20+5\right)^3.4^5}=\frac{25000000-5000000+80000000}{15625.4^5}=\frac{100000000}{16000000}=\frac{25}{4}\)
Ta có: \(A=\dfrac{3^6.21^{12}}{175^9.7^3}=\dfrac{3^6.3^{12}.7^{12}}{5^{18}.7^9.7^3}=\dfrac{3^{18}.7^{12}}{5^{18}.7^{12}}=\dfrac{3^{18}}{5^{18}}=\left(\dfrac{3}{5}\right)^{18}\)
\(B=\dfrac{3^{10}.6^7.4}{10^9.5^8}=\dfrac{3^{10}.2^7.3^7.2^2}{2^9.5^9.5^8}=\dfrac{3^{17}.2^9}{2^9.5^{17}}=\dfrac{3^{17}}{5^{17}}=\left(\dfrac{3}{5}\right)^{17}\)
Vì \(\left(\dfrac{3}{5}\right)^{18}< \left(\dfrac{3}{5}\right)^{17}\Rightarrow A< B\)
Vậy A < B
B = 3 99.96 − 3 96.93 − 3 93.90 − ... − 3 7.4 − 3 4 = 3 99.96 − 3 96.93 + 3 96.93 + ... + 3 7.4 + 3 4.1 = 3 99.96 − 3 1.4 + 3 4.7 + ... + 3 90.93 + 3 93.96 = 3 99.96 − 1 − 1 4 + 1 4 − 1 7 + ... + 1 90 − 1 93 + 1 93 − 1 96 = 1 96 − 1 99 − 1 − 1 96 = 1 96 − 1 99 − 1 + 1 96 = 1 48 − 1 − 1 99 = − 47 48 − 1 99 = − 1567 1584