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T
13 tháng 7 2019
#)Giải :
a)\(2009^{\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-15^3\right)}=2009^{\left(1000-1^3\right)...\left(1000-10^3\right)...\left(1000-15^3\right)}=2009^0=1\)
b)\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)=\left(\frac{1}{125}-\frac{1}{1^3}\right)...\left(\frac{1}{125}-\frac{1}{5^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)=\left(\frac{1}{125}-\frac{1}{1^3}\right)...0...\left(\frac{1}{125}-\frac{1}{25^3}\right)=0\)
15 tháng 7 2019
\(a,\left[\left(-\frac{1}{2}\right)^3-\left(\frac{3}{4}\right)^3.\left(-2\right)^2\right]:\left[2.\left(-1\right)^5+\left(\frac{3}{4}\right)^2-\frac{3}{8}\right]\)
\(=\left[\left(-\frac{1}{8}\right)-\frac{27}{64}.4\right]:\left[2.\left(-1\right)+\frac{9}{16}-\frac{3}{8}\right]\)
\(=\left[\left(-\frac{1}{8}-\frac{27}{16}\right)\right]:\left[-2+\frac{9}{16}-\frac{3}{8}\right]\)
\(=\frac{-2-27}{16}:\frac{-32+9-6}{16}\)
\(=-\frac{29}{16}:\frac{-29}{16}=1\)
\(b,\left[\left(\frac{4}{3}\right)^{-2}\left(\frac{3}{2}\right)^4\right]:\left(\frac{3}{2}\right)^6\)
\(=\left(\frac{9}{16}.\frac{81}{16}\right):\frac{729}{64}\)
\(=\frac{729}{64}:\frac{729}{64}=1\)
22 tháng 1 2019
\(1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+\frac{1}{4}.\left(1+2+3+4\right)+...+\frac{1}{20}.\left(1+...+20\right).\)
\(=1+\frac{3}{2}+\frac{6}{3}+\frac{10}{4}+...+\frac{210}{20}\)
\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{21}{2}\)
\(=\frac{2+3+4+5+...+21}{2}=\frac{230}{2}=115\)
12 tháng 12 2019
\(\left(\frac{1}{2}\right)^{15}\cdot\left(\frac{1}{4}\right)^{20}=\left(\frac{1}{2}\right)^{15}\cdot\left[\left(\frac{1}{2}\right)^2\right]^{20}=\left(\frac{1}{2}\right)^{15}\cdot\left(\frac{1}{2}\right)^{40}=\left(\frac{1}{2}\right)^{15+40}=\left(\frac{1}{2}\right)^{55}\)
\(\left(\frac{1}{9}\right)^{25}:\left(\frac{1}{3}\right)^{30}=\left[\left(\frac{1}{3}\right)^2\right]^{25}:\left(\frac{1}{3}\right)^{30}=\left(\frac{1}{3}\right)^{50}:\left(\frac{1}{3}\right)^{30}=\left(\frac{1}{3}\right)^{50-30}=\left(\frac{1}{3}\right)^{20}\)
NẾU THẤY ĐÚNG THÌ NHỚ K CHO MÌNH VỚI ĐÓ !!! :33
12 tháng 9 2018
\(\frac{1}{20}\left(x-\frac{8}{15}\right)=-\frac{1}{30}\) \(\left(28+\frac{1}{5}\right).\left(\frac{3}{5}.x+\frac{4}{7}\right)=0\)
\(x-\frac{8}{15}=-\frac{1}{30}:\frac{1}{20}\) \(\frac{141}{5}.\left(\frac{3}{5}.x+\frac{4}{7}\right)=0\)
\(x-\frac{8}{15}=-\frac{2}{3}\) \(\frac{3}{5}.x+\frac{4}{7}=0\)
\(x=-\frac{2}{3}+\frac{8}{15}\) \(\frac{3}{5}.x=-\frac{4}{7}\)
\(x=-\frac{2}{15}\) \(x=-\frac{20}{21}\)
\(\left(\frac{1}{2}\right)^{15}.\left(\frac{1}{4}\right)^{20}\)
\(=\left(\frac{1}{2}\right)^{15}.\left[\left(\frac{1}{2}\right)^2\right]^{20}\)
\(=\left(\frac{1}{2}\right)^{15}.\left(\frac{1}{2}\right)^{40}\)
\(=\left(\frac{1}{2}\right)^{15+40}=\left(\frac{1}{2}\right)^{55}=\frac{1}{2^{55}}\)
\(\left(\frac{1}{2}\right)^{15}.\left(\frac{1}{4}\right)^{20} =\left(\frac{1}{2}\right)^{15}.\left(\frac{1}{2}\right)^{40}=\left(\frac{1}{2}\right)^{55}\)