\(\dfrac{2^3.49^3}{14^2.7^5}=\dfrac{2^3.7^6}{7^2.2^2.7^5}=\dfrac{2^3.7^6}{7^7.2^2}=\dfrac{2}{7}\)

a) \(\dfrac{2}{7}+\dfrac{4}{7}=\dfrac{2+4}{7}=\dfrac{6}{7}\)

b) \(\dfrac{23}{13}+\dfrac{8}{13}=\dfrac{23+8}{13}=\dfrac{31}{13}\)

c) \(\dfrac{27}{125}+\dfrac{16}{125}=\dfrac{27+16}{125}=\dfrac{43}{125}\)

a)\(\dfrac{2}{7}\) + \(\dfrac{4}{7}\) =  \(\dfrac{6}{7}\)  

b)\(\dfrac{23}{13}\) + \(\dfrac{8}{13}\) = \(\dfrac{31}{13}\)          

c)\(\dfrac{27}{125}\) + \(\dfrac{16}{125}\) = \(\dfrac{43}{125}\)

\(B=\dfrac{35^3+5\cdot35^2-5^3\cdot7}{10\cdot70^2+10^2\cdot70-10^3}=\dfrac{\left(5\cdot7\right)^3+5\cdot\left(5\cdot7\right)^2-5^3\cdot7}{2\cdot5\cdot\left(2\cdot5\cdot7\right)^2+\left(2\cdot5\right)^2\cdot2\cdot5\cdot7-\left(2\cdot5\right)^3}=\dfrac{5^3\cdot7^3+5\cdot5^2\cdot7^2-5^3\cdot7}{2\cdot5\cdot2^2\cdot5^2\cdot7^2+2^2\cdot5^2\cdot2\cdot5\cdot7-2^3\cdot5^3}=\dfrac{5^3\cdot7^3+5^3\cdot7^2-5^3\cdot7}{2^3\cdot5^3\cdot7^2+2^3\cdot5^3\cdot7-2^3\cdot5^3}=\dfrac{5^3\left(7^3+7^2-7\right)}{2^3\cdot5^3\left(7^2+7-1\right)}=\dfrac{343+49-7}{8\cdot\left(49+7-1\right)}=\dfrac{385}{8\cdot55}=\dfrac{385}{440}=\dfrac{7}{8}\)

Vậy \(B=\dfrac{7}{8}\)

\(a,\dfrac{5^{16}\cdot27^7}{125^5\cdot9^{11}}=\dfrac{5^{16}\cdot\left(3^3\right)^7}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}\)

\(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)

\(b,\left(-0,2\right)^2\cdot5-\dfrac{2^{13}\cdot27^3}{4^6\cdot9^5}\)

\(=0,04\cdot5-\dfrac{2^{13}\cdot\left(3^3\right)^3}{\left(2^2\right)^6\cdot\left(3^2\right)^5}\)

\(=0,2-\dfrac{2^{13}\cdot3^9}{2^{12}\cdot3^{10}}\)

\(=0,2-\dfrac{2}{3}\)

\(=-\dfrac{7}{15}\)

\(c,\dfrac{5^6+2^2\cdot25^3+2^3\cdot125^2}{26\cdot5^6}\)

\(=\dfrac{5^6+2^2\cdot\left(5^2\right)^3+2^3\cdot\left(5^3\right)^2}{5^6\cdot26}\)

\(=\dfrac{5^6+4\cdot5^6+8\cdot5^6}{5^6\cdot26}\)

\(=\dfrac{5^6\left(1+4+8\right)}{5^6\cdot26}\)

\(=\dfrac{13}{26}\)

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

#\(Toru\)

\(a,\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{\left(5^2\right)^8.9^7.3^7}{25^5.5^5.9^{11}}\\ =\dfrac{25^8.9^7.\left(3^2\right)^3.3}{25^5.\left(5^2\right)^2.5.9^{11}}=\dfrac{25^8.9^7.9^3.3}{25^5.25^2.5.9^{11}}\\ =\dfrac{25^8.9^{10}.3}{25^7.5.9^{11}}=\dfrac{25^7.9^{10}.25.3}{25^7.9^{10}.5.9}\\ =\dfrac{25.3}{5.9}=\dfrac{5.5.3}{5.3.3}=\dfrac{5}{3}\)

232/301

Gợi ý cho bn: Tách chúng ra nhé, rồi rút gọn số có ở trên cả tử và mẫu.

\(=\dfrac{2^{12}.3^{15}.7^{30}-31.2^{12}.3^{12}.3^2.7^{28}}{2^{11}.3^{14}.7^{14}.7^{15}+2^{12}.3^{15}.7^{30}}=\)

\(=\dfrac{2^{12}.3^{15}.7^{30}-31.2^{12}.3^{14}.7^{28}}{2^{11}.3^{14}.7^{29}+2^{12}.3^{15}.7^{30}}=\)

\(=\dfrac{2^{11}.3^{14}.7^{28}\left(2.3.7^2-31.2\right)}{2^{11}.3^{14}.7^{28}\left(7+2.3\right)}=\dfrac{2.3.7^2-31.2}{7+2.3}=\dfrac{232}{13}\)

1) \(\dfrac{17}{5}\cdot\dfrac{-31}{125}\cdot\dfrac{1}{2}\cdot\dfrac{10}{17}\cdot\dfrac{-1}{2^3}\)

\(=\dfrac{17\cdot\left(-31\right)\cdot1\cdot2\cdot5\cdot\left(-1\right)}{5\cdot125\cdot2\cdot17\cdot8}\)

\(=\dfrac{\left(-31\right)\left(-1\right)}{125\cdot8}\\ =\dfrac{31}{1000}\)

\(A=\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right)\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right)\left(\dfrac{1}{125}-\dfrac{1}{3^3}\right)....\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)\)

\(A=\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right)\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right)....\left(\dfrac{1}{125}-\dfrac{1}{5^3}\right).....\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)\)

\(A=\left(\dfrac{1}{125}-\dfrac{1}{1^3}\right)\left(\dfrac{1}{125}-\dfrac{1}{2^3}\right)....0......\left(\dfrac{1}{125}-\dfrac{1}{25^3}\right)\)

\(A=0\)

Ta có: \(\left|97\dfrac{2}{3}-125\dfrac{3}{5}\right|+97\dfrac{2}{5}-125\dfrac{1}{3}\)

\(=\left|97+\dfrac{2}{3}-125-\dfrac{3}{5}\right|+97+\dfrac{2}{5}-125-\dfrac{1}{3}\)

\(=\left|-28+\dfrac{1}{15}\right|-28+\dfrac{1}{15}\)

\(=\left|\dfrac{1}{15}-28\right|-28+\dfrac{1}{15}\)

\(=28-\dfrac{1}{15}-28+\dfrac{1}{15}\)

\(=0\)

\(A=4^3-6^3:6^2+11\cdot3^2\\ =64-6+11\cdot9\\ =58+99\\ =157\\ B=5\cdot35-5^2\cdot2\\ =5\cdot\left(35-10\right)\\ =5\cdot25\\ =125\\ C=\left(7-3^3:3^2\right):2^2+99\\ =\left(7-3\right):4+99\\ =4:4+99\\ =1+99=100\\ D=2^7:2^2+5^4:5^3\cdot2^4-3\cdot2^5\\ =2^5+5\cdot2^4-6\cdot2^4\\ =2^4\cdot\left(2+5-6\right)\\ =2^4\\ =16\)

đợi tý

a) 157

b) 125

c) 100

d) 16