A=5/9/10:3/2-(2/1/3.4/1/2-2.2/1/3):7/4
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TD
1
VN
Võ Ngọc Phương
VIP
20 tháng 9 2023
a) \(2^5+5.13-3.2^3\)
\(=32+5.13-3.8\)
\(=32+65-24\)
\(=97-24\)
\(=73\)
b) \(5^{13}:5^{10}-5^2.2^2\)
\(=5^3-25.4\)
\(=125-100\)
\(=25\)
c) \(4^5:4^3-3^9:3^7+5^0\)
\(=4^2-3^2+1\)
\(=16-9+1\)
\(=7+1\)
\(=8\)
NM
0
24 tháng 10 2016
Bài 1:
Ta có:
\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}\)
\(=\frac{3}{1.4}+\frac{5}{4.9}+\frac{7}{9.16}+...+\frac{19}{81.100}\)
\(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+...+\frac{1}{81}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
Mà \(\frac{99}{100}< 1\)
\(\Rightarrow\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}< 1\left(đpcm\right)\)
TT
7 tháng 10 2017
b. \(\left(\dfrac{3^2}{9}.\dfrac{3^3}{81}\right)^{12}:\left(\dfrac{3^6}{81^2}\right)^{10}\)
\(=\left(1.\dfrac{1}{3}\right)^{12}:\left(\dfrac{1}{9}\right)^{10}\)
\(=\left(\dfrac{1}{3}\right)^{12}:\left(\dfrac{1}{9}\right)^{10}\)
\(=\left[\left(\dfrac{1}{3}\right)^2\right]^6:\left(\dfrac{1}{9}\right)^{10}\)
\(=\left(\dfrac{1}{9}\right)^6:\left(\dfrac{1}{9}\right)^{10}\)
\(=\left(\dfrac{1}{9}\right)^{-4}=6561\)
\(A=5\frac{9}{10}:\frac{3}{2}-\left(2\frac{1}{3}.4\frac{1}{2}-2.2\frac{1}{3}\right):\frac{7}{4}\)
\(A=\frac{59}{10}:\frac{3}{2}-\left(\frac{7}{3}.\frac{9}{2}-2.\frac{7}{3}\right):\frac{7}{4}\)
\(A=\frac{59}{15}-\left(\frac{21}{2}-\frac{14}{3}\right):\frac{7}{4}\)
\(A=\frac{59}{15}-\frac{35}{6}:\frac{7}{4}\)
\(A=\frac{59}{15}-\frac{10}{3}\)
\(A=\frac{3}{5}\)