Thực hiện phép tính:
\(\frac{5^3.5^8}{25^4}\)
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BC
31 tháng 3 2019
a)Ta có:
\(A=4\frac{25}{16}+25\left(\frac{9}{16}:\frac{125}{64}\right):\frac{-27}{8}\)
\(\Rightarrow A=\frac{89}{16}+25.\frac{36}{125}:\frac{-27}{8}\)
\(\Rightarrow A=\frac{89}{16}+\frac{36}{5}:\frac{-27}{8}\)
\(\Rightarrow A=\frac{89}{16}+\frac{-32}{15}\)
\(\Rightarrow A=\frac{823}{240}\)
Vậy A=.....
b)Ta có:
\(C=\frac{2^3}{3.5}+\frac{2^3}{5.7}+\frac{2^3}{7.9}+...+\frac{2^3}{101.103}\)
\(\Rightarrow C=\frac{2^2.2}{3.5}+\frac{2^2.2}{5.7}+\frac{2^2.2}{7.9}+...+\frac{2^2.2}{101.103}\)
\(\Rightarrow C=2^2\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{101.103}\right)\)
\(\Rightarrow C=4\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{101}-\frac{1}{103}\right)\)
\(\Rightarrow C=4\left(\frac{1}{3}-\frac{1}{103}\right)\)
\(\Rightarrow C=4.\frac{100}{309}\)
\(\Rightarrow C=\frac{400}{309}\)
Vậy C=.....
LD
1
HT
11 tháng 12 2016
\(\frac{8^{20}+4^{20}}{4^{25}+64^5}\)=\(\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)=\(\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)=\(\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}\)=\(\frac{2^{40}}{2^{30}}\)= 210
VV
6
22 tháng 7 2017
= \(\frac{5^6.5^5}{6.5^{10}}\) = \(\frac{5^{11}}{6.5^{10}}\)= \(\frac{5}{6}\)
TP
22 tháng 7 2017
\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
Phân tích từ số:
\(\frac{2^{12}.3^5-4^2.4^4.3^4}{2^{12}.3.3^5+4^2.4^4.3.3^4}=\frac{1}{6}\)
\(\frac{5^9.5.7^3-5^9.5.7^3.7}{5^9.7^3+5^9.2^3.7^3}=\frac{-10}{3}\)
Sau khi rút gọn là:
\(\frac{1}{6}-\left(-\frac{10}{3}\right)=\frac{1}{6}+\frac{10}{3}=\frac{7}{2}\)
27 tháng 4 2019
\(\left(6-\frac{14}{5}\right).\frac{25}{8}-\frac{8}{5}:\frac{1}{4}\)
=\(\left(\frac{6}{1}+\frac{-14}{5}\right).\frac{25}{8}-\frac{8}{5}:\frac{1}{4}\)
=\(\frac{16}{5}.\frac{25}{8}-\frac{8}{5}:\frac{1}{4}\)
=\(\frac{16.25}{5.8}-\frac{8}{5}.\frac{4}{1}\)
=\(\frac{2.8.5.5}{5.8}-\frac{32}{5}\)
=\(2.5-\frac{32}{5}\)
=\(10-\frac{32}{5}\)
=\(\frac{10}{10}+\frac{-32}{5}\)
=\(\frac{10}{10}+\frac{-46}{10}\)
=\(\frac{-36}{10}\)
=\(\frac{18}{5}\)
\(\frac{5^3.5^8}{25^4}\)
\(=\frac{5^{11}}{25^4}\)
\(=\frac{48828125}{390625}\)
\(\frac{5^3.5^8}{25^4}=\frac{5^8.5^3}{\left(5^2\right)^4}\)
\(\Rightarrow\frac{5^8.5^3}{5^8}=5^3=125\)
Hk tốt