1) Sửa đề :
\(\frac{10^3+5\cdot10^2+5^3}{6^3+3\cdot6^2+3^3}=\frac{10^3+5\cdot5^2\cdot2^2+5^3}{6^3+3\cdot2^2\cdot3^2+3^3}=\frac{5^3\cdot\left(2^3+2^2+1\right)}{3^3\cdot\left(2^3+2^2+1\right)}=\frac{5^3}{3^3}\)
2) Sửa đề :
\(\frac{5^3+3\cdot5^2}{-8}=\frac{5^2\cdot\left(5+3\right)}{-8}=\frac{-5^2\cdot8}{8}=-5^2=-25\)
\(\frac{10+\frac{9}{2}+\frac{8}{3}+\frac{7}{4}+ \frac{6}{5}+\frac{5}{6}+\frac{4}{7}+\frac{3}{8}+\frac{2}{9}+\frac{1}{10}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}+\frac{1}{11}}\)
Rút gọn biểu thức :
\(\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)
\(\frac{\left(5^2.6^{11}.16^2+6^2.12^6.15^2\right).10}{2.6^{12}.10^4-81^2.960^3}\)
Giải ra bn nhé !
Tính hợp lí :
\(\frac{1}{7}.\frac{1}{3}+\frac{1}{7}.\frac{1}{2}-\frac{1}{7}\)
Rút gọn rồi tính :
1) \(\frac{5^4\times9^5}{15^3\times27^3}\)
2) \(\frac{8^8\times3^{14}}{9^6\times2^{20}}\)
3) \(\frac{4^{10}\times25^7}{5^{14}\times8^6}\)
4) \(\frac{25^7\times2^{15}}{8^5\times5^{12}}\)
1.tính các biểu thức sau bằng một cách hợp lí
a.\(\frac{108}{119}.\frac{107}{211}+\frac{108}{119}.\frac{104}{211}\)
b.\(\frac{15}{19}.\frac{27}{33}+\frac{15}{19}.\frac{19}{33}-\frac{15}{19}.\frac{13}{33}\)
c.\(\frac{-4}{5}.\frac{13}{10}+\frac{-4}{5}.\frac{7}{10}-\frac{-4}{5}\)
d.\(\frac{\frac{-2}{7}-\frac{-2}{15}+\frac{-2}{39}}{\frac{5}{7}-\frac{5}{15}+\frac{5}{39}}\)
e.\(\frac{3}{5}.\frac{15}{7}-\frac{15}{7}.\frac{8}{5}\)
f.\(\frac{2}{3}+\frac{1}{3}.\left(\frac{-4}{9}+\frac{5}{6}\right):\frac{7}{12}\)
h.\(\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}\)
g.\(\frac{3}{-4}+\frac{2}{7}+\frac{-1}{4}+\frac{5}{7}+\frac{21}{22}.\frac{66}{7}\)
k.\(\frac{27.18+27.103-120.27}{15.33+33.12}\)
l.\(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
Biết \(2-\frac{3}{4-\frac{5}{6-\frac{7}{8-\frac{9}{10}}}}=2-\frac{3}{4-\frac{5}{x}}\). Tìm x.
Bài tập Violympic môn toán lớp 6 :
Nội dung: Nâng cao và ko nâng cao
Bài 1*: Rút gọn biểu thức sau:
a) A = 1 - 2 + 3 - 4 + 5 - 6 + ... + 2021 - 2022 + 2023
b) B = 1 - 4 + 7 - 10 + ... + 307 - 310 + 313
c) C = -2194 . 21952195 + 2195 . 21942194
Bài 2: Thực hiện phép tính 1 cách hợp lí:
a, ( -5 ) . ( -6 ) . ( -4 ) . 2
b, ( -3 ) . 2
\(\left(20+9\frac{1}{4}\right):2\frac{1}{4}\) \(\left(6-2\frac{4}{5}\right).3\frac{1}{8}-1\frac{3}{5}:\frac{1}{4}\)
\(\frac{32}{15}:\left(-1\frac{1}{5}+1\frac{1}{3}\right)\) \(0,2.\frac{15}{36}-\left(\frac{2}{5}=\frac{2}{3}\right):1\frac{1}{5}\)
\(\frac{-3}{7}.\frac{5}{9}+\frac{4}{9}.\frac{-3}{7}+2\frac{3}{7}\) \(0,7.2\frac{2}{3}.20.0,375.\frac{5}{8}\)
Bài 1: rút gọn các phân số sau:
a) \(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}\)
b) \(\frac{-11^5.13^7}{11^5.13^8}\)
c) \(\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}\)
d) \(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}\)
1, RÚT GỌN BIỂU THỨC
a, (a^3)^5 : a^10 . (a^3)^4
b, (2^3)^4 . (2^4)^3 : 2^26
c, 4^9 : 4^4 . (a^2)^6
