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\(\left(\dfrac{2}{3}\right)^3.\left(\dfrac{-3}{4}\right)^2.\left(-1\right)^{2013}=\dfrac{8}{27}.\dfrac{9}{16}.\left(-1\right)=-\dfrac{1}{6}\)
\(\left(\dfrac{1}{5}\right)^{15}.\left(\dfrac{1}{4}\right)^{20}=\dfrac{1}{5^{12}}.\dfrac{1}{4^{20}}=5^{-12}.4^{-20}=125^{-4}.1024^{-4}=\left(125.1024\right)^{-4}=128000^{-4}\)
\(\dfrac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}=\dfrac{2^{12}.3^{10}+2^3.3.5.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}+2^{12}.2^{10}.5}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3+1\right)}=\dfrac{2.6}{3.7}=\dfrac{4}{7}\)
Phân tích ra : VD : 415=(22)15=22.15=230
Nếu làm thế này thì sẽ dể hơn vì sẽ có nhiều lũy thừa giống nhau và dễ chiệt tiêu hơn nhé bạn >
a) \(\frac{7.12^3+2.12^3}{4^6.3^{11}}=\frac{12^3.\left(7+2\right)}{\left(2^2\right)^6.3^{11}}=\frac{\left(2^2.3\right)^3.3^2}{2^{12}.3^{11}}=\frac{2^6.3^5}{2^{12}.3^{11}}=\frac{1}{2^6.3^6}=\frac{1}{6^6}\)
\(\frac{-17.10+17.6}{18.11+18.6}=\frac{17.\left(-10+6\right)}{18.\left(11+6\right)}=\frac{17.\left(-4\right)}{18.17}=\frac{-2}{9}\)
\(\frac{6.7.8.10}{9.12.14.15}=\frac{2.3.7.2^3.2.5}{3^2.3.2^2.2.7.3.5}=\frac{2^5.3.5.7}{2^3.3^4.5.7}=\frac{2^2}{3^3}=\frac{4}{27}\)
phần b viết khó hiểu, phải viết phân số như a đàng hoàng
Câu 3:
a) \(\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}\)
\(\dfrac{-16}{20}=\dfrac{-16:4}{20:4}=\dfrac{-4}{5}\)
b) \(\dfrac{21}{105}=\dfrac{21:21}{105:21}=\dfrac{1}{5}\)
\(\dfrac{35}{150}=\dfrac{35:5}{150:5}=\dfrac{7}{30}\)
Câu 4:
a) \(\dfrac{3}{10}+\dfrac{5}{10}=\dfrac{3+5}{10}=\dfrac{8}{10}=\dfrac{4}{5}\)
b) Ta có: \(\left(-27\right)\cdot36+64\cdot\left(-27\right)+23\cdot\left(-100\right)\)
\(=\left(-27\right)\cdot\left(64+36\right)+23\cdot\left(-100\right)\)
\(=-27\cdot100-23\cdot100\)
\(=100\left(-27-23\right)\)
\(=-50\cdot100=-5000\)
c) \(\dfrac{5}{8}+\dfrac{3}{12}=\dfrac{15}{24}+\dfrac{6}{24}=\dfrac{21}{24}=\dfrac{7}{8}\)
d) Ta có: \(\dfrac{-2}{17}+\dfrac{3}{19}+\dfrac{-15}{17}+\dfrac{16}{19}+\dfrac{5}{6}\)
\(=\left(-\dfrac{2}{17}+\dfrac{-15}{17}\right)+\left(\dfrac{3}{19}+\dfrac{16}{19}\right)+\dfrac{5}{6}\)
\(=-1+1+\dfrac{5}{6}\)
\(=\dfrac{5}{6}\)
Rút gọn rồi tính:
a) \(\frac{8}{10}-\frac{12}{9}+\frac{10}{15}\)
\(=\frac{4}{5}-\frac{4}{3}+\frac{2}{3}\)
\(=\frac{12-20+10}{15}\)
\(=\frac{2}{15}\)
b) \(\left(\frac{20}{16}-\frac{15}{12}\right)\div\left(\frac{6}{8}-\frac{9}{12}\right)\)
\(=\left(\frac{5}{4}-\frac{5}{4}\right)\div\left(\frac{3}{4}-\frac{3}{4}\right)\)
\(=1\div1\)
\(=1\)
\(a,\frac{8}{10}-\frac{12}{9}+\frac{10}{15}\)
\(=\frac{4}{5}-\frac{4}{3}+\frac{2}{3}\)
\(=\frac{4}{5}-\left(\frac{4}{3}+\frac{2}{3}\right)\)
\(=\frac{4}{5}-2\)
\(=\frac{4}{5}+\frac{-10}{5}\)
\(=\frac{-6}{5}\)
\(b,\left(\frac{20}{16}-\frac{15}{12}\right):\left(\frac{6}{8}-\frac{9}{12}\right)\)
\(=\left(\frac{5}{4}-\frac{5}{4}\right):\left(\frac{3}{4}-\frac{3}{4}\right)\)
\(=0:0\)
\(=0\)
Bạn đăng lên H.vn thử xem . Trên đấy có nhiều người trả lời giúp hơn đấy mà còn nhanh hơn nữa.
\(A=\dfrac{2.3.\left(2^3\right)^6.3^{20}-2^2.5.3^{20}.\left(2^2\right)^8}{7.2^2.2^{16}.\left(3^2\right)^{10}-2.3^2.2^{18}.\left(3^3\right)^6}\)
\(=\dfrac{2.3.2^{18}.3^{20}-5.2^2.3^{20}.2^{16}}{7.2^2.2^{16}.3^{20}-2.3^2.2^{18}.3^{18}}=\dfrac{2^{19}.3^{21}-5.2^{18}.3^{20}}{7.2^{18}.3^{20}-2^{20}.3^{20}}\)
\(=\dfrac{2^{18}.3^{20}\left(2.3-5\right)}{2^{18}.3^{20}.\left(7-2^2\right)}=\dfrac{2.3-5}{7-4}=\dfrac{1}{3}\)