B=\(\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9+2^{10}.3^{10}}\)
\(\dfrac{2^{19}.27^3-15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\dfrac{2^{19}.\left(3^3\right)^3-3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}=\dfrac{2^{19}.3^9-5.2^{18}.3^9}{2^{19}.3^9+2^{20}.3^{10}}=\dfrac{2^{18}.3^9\left(2-5\right)}{2^{19}.3^9\left(1+6\right)}=\dfrac{-3}{2.7}=-\dfrac{3}{14}\)
\(\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\\ =\dfrac{2^{19}.3^9+5.2^{18}.3^9}{2^9.3^9+2^{20}.3^{10}}\\ =\dfrac{2^{18}.3^9\left(2+5\right)}{2^9.3^9\left(2^{11}.3+1\right)}\\ =\dfrac{2^9.7}{2^9.12+1}=\dfrac{7}{13}\)
Tính biểu thức sau
\(\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\dfrac{2^{19}\cdot3^9+2^{18}\cdot3^9\cdot5}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}=\dfrac{2^{18}\cdot3^9\left(5+2\right)}{2^{19}\cdot3^9\left(1+2\cdot3\right)}=\dfrac{1}{2}\)
Bài 3: Rút gọn các phân số sau:
a) \(\dfrac{10.11+50.55+70.77}{11.12+55.60+77.84}\)
b) \(\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
(Tớ cần lời giải tính nhanh và hợp lý ạ,giúp tớ vớii)
A= \(\dfrac{10.11.\left(1+5.5+7.7\right)}{11.12.\left(1+5.5+7.7\right)}=\dfrac{10}{12}=\dfrac{5}{6}\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+5.3.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^9+5.3.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}=\frac{2^{19}.3^9+5.2^{18}.3^9}{2^{19}.3^9+2^{20}.3^{10}}=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{2^{18}.3^9}{2^{19}.3^9}=\frac{1}{2}\)
P/s: Sai gì bỏ qua =)
rút gọn: \(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(=\frac{2^{19}.3^9.\left(1+5\right)}{2^{19}.3^9.\left(1+2.3\right)}=\frac{6}{7}\)
Rút gọn
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(=\frac{2^{19}.3^9+3^9.5.2^{18}}{2^9.3^9.2^{10}+2^{20}.3^{10}}=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{1}{2}\)
1, So sánh A và B biết A=\(\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\) B=\(\dfrac{4}{35}+\dfrac{4}{63}+\dfrac{4}{99}+\dfrac{4}{143}+\dfrac{4}{195}\) ( GIÚP Mk Với Mk Đang Cần Gấp )
may mà m đăng để t đỡ phải viết (mỏi tay) Nguyen Ngoc Linh
\(A=\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+2^{12}}\)
\(=\dfrac{2^{19}.3^9+5.2^{18}.3^9}{2^9.3^{19}+2^{12}}=\dfrac{2^{10}+5.2^8}{3^{10}+2^3}=\dfrac{2^7+5.2^5}{3^{10}}\)
\(B=\dfrac{4}{35}+\dfrac{4}{63}+\dfrac{4}{99}+\dfrac{4}{143}+\dfrac{4}{195}\)
\(=2\left(\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}+\dfrac{2}{13.15}\right)\)
\(=2.\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}\right)\)
\(=2\left(\dfrac{1}{5}-\dfrac{1}{15}\right)=2\left(\dfrac{2}{15}\right)\)=\(\dfrac{4}{15}\)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\) Rút gọn :
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
= \(\frac{2^{19}.3^9+5.2^{18}.3^9}{6^9.2^{10}+2^{10}.6^{10}}\)
=\(\frac{\left(2^{18}.3^9\right)\left(2+5\right)}{\left(6^9.2^{10}\right)\left(1+6\right)}\)
=\(\frac{7\left(2^{18}.3^9\right)}{7\left(3^9.2^9.2^{10}\right)}\)
= \(\frac{7\left(2^{18}.3^9\right)}{7\left(3^9.2^{19}\right)}\)
= \(\frac{1}{2}\)