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e: \(=\dfrac{2^{10}\cdot3^9-2^9\cdot3^8}{2^{10}\cdot3^8}=\dfrac{2^9\cdot3^8\left(2\cdot3-1\right)}{2^{10}\cdot3^8}=\dfrac{5}{2}\)
g: \(=125+\dfrac{3}{5}-97-\dfrac{2}{3}+97+\dfrac{2}{5}-125-\dfrac{1}{3}=0\)
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\(5:\left(-\dfrac{5}{2}\right)^2+\dfrac{2}{15}\cdot\sqrt{\dfrac{9}{4}}-\left(-2020\right)^0+\left|-0,25\right|\)
\(=5:\dfrac{25}{4}+\dfrac{2}{15}\cdot\dfrac{3}{2}-1+0,25\)
\(=5\cdot\dfrac{4}{25}+\dfrac{3}{15}-0,75\)
\(=\dfrac{4}{5}+\dfrac{1}{5}-\dfrac{3}{4}\)
\(=1-\dfrac{3}{4}\)
\(=\dfrac{1}{4}\)
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\(\sqrt{25}\)= 5 , - \(\sqrt{4}\) = 2 => 5-3*2:9= 5-6:9= 5-\(\dfrac{2}{3}\)= \(\dfrac{13}{3}\)
ta có \(\sqrt{25}-3\sqrt{\dfrac{4}{9}}\)
\(\Rightarrow\sqrt{25}.2\)
\(\Rightarrow5.2=10\)
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ta có \(2^7.9^2:3^3.2^5\)
=\(2^7.3^4:3^2.2^5\)
=\(\left(2^7.2^5\right):\left(3^4.3^3\right)\)
=\(2^{12}:3^7\)
=\(4096:2187\)=\(1,872885231\approx2\)
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\(-\dfrac{3}{8}-\left(-\dfrac{3}{24}\right)\)
\(=-\dfrac{3}{8}+\dfrac{3}{24}\)
\(=-\dfrac{9}{24}+\dfrac{3}{24}\)
\(=\dfrac{-9+3}{24}\)
\(=-\dfrac{6}{24}\)
\(=-\dfrac{1}{4}\)
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\(\dfrac{4}{5}-\dfrac{2}{9}\times\left(-3\right)^2+\dfrac{9}{2}\div3\)
\(=\dfrac{4}{5}-\dfrac{2}{9}\times9+\dfrac{3}{2}\)
\(=\dfrac{4}{5}-2+\dfrac{3}{2}\)
\(=-\dfrac{6}{5}+\dfrac{3}{2}\)
\(=\dfrac{3}{10}\)
\(\dfrac{4}{5}-\dfrac{2}{9}.\left(-3\right)^2+\dfrac{9}{2}:3\)
\(=\dfrac{4}{5}-\dfrac{2}{9}.9+\dfrac{9}{2}.\dfrac{1}{3}\)
\(=\dfrac{4}{5}-2+\dfrac{3}{2}\)
\(=\dfrac{8}{10}-\dfrac{20}{10}+\dfrac{15}{10}\)
\(=\dfrac{3}{10}\)
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Dữ liệu cho trong bảng không hợp lí vì tổng tỉ lệ phần trăm của tất cả các thành phần là 120% (khác 100%)
a) \(\left(\dfrac{3}{8}-\dfrac{1}{5}-\dfrac{1}{3}\right)+\left(\dfrac{5}{8}-1\dfrac{3}{7}-\dfrac{4}{7}\right)+\dfrac{1}{3}\)
\(=\dfrac{3}{8}-\dfrac{1}{5}-\dfrac{1}{3}+\dfrac{5}{8}-\dfrac{10}{7}-\dfrac{4}{7}+\dfrac{1}{3}\)
\(=\left(\dfrac{3}{8}+\dfrac{5}{8}\right)+\left(\dfrac{-1}{3}+\dfrac{1}{3}\right)+\left(\dfrac{-10}{7}-\dfrac{4}{7}\right)-\dfrac{1}{5}\)
\(=1+0+\left(-2\right)-\dfrac{1}{5}\)
\(=-1-\dfrac{1}{5}\)
\(=\dfrac{-6}{5}\)
b) \(-24.\left(\dfrac{1}{3}-\dfrac{1}{4}\right)^2-1,5\)
\(=-24.\left(\dfrac{1}{12}\right)^2-\dfrac{3}{2}\)
\(=-24.\dfrac{1}{144}-\dfrac{3}{2}\)
\(=\dfrac{-1}{6}-\dfrac{3}{2}=\dfrac{-1}{6}-\dfrac{9}{6}=\dfrac{-10}{6}=\dfrac{-5}{3}\)
c) \(2^2-\left(-\dfrac{5}{7}\right)^0+\left(\dfrac{1}{3}\right)^4.3^6\)
\(=4-1+\dfrac{1}{81}.729\)
\(=4-1+9\)
\(=3+9=12\)
d) \(23\dfrac{1}{3}:\left(\dfrac{-5}{7}\right)+13\dfrac{1}{3}:\dfrac{5}{7}\)
\(=\dfrac{-70}{3}.\dfrac{7}{5}+\dfrac{40}{3}.\dfrac{7}{5}\)
\(=\dfrac{7}{5}\left(\dfrac{-70}{3}-\dfrac{40}{3}\right)\)
\(=\dfrac{7}{5}.\left(-10\right)\)
\(=-14\)
e) \(\dfrac{3}{4}.\dfrac{8}{5}+\dfrac{6}{15}:\dfrac{4}{3}-1\dfrac{2}{5}:1\dfrac{1}{3}\)
\(=\dfrac{3}{4}.\dfrac{8}{5}+\dfrac{6}{15}.\dfrac{3}{4}-\dfrac{7}{5}.\dfrac{3}{4}\)
\(=\dfrac{3}{4}\left(\dfrac{8}{5}+\dfrac{6}{15}-\dfrac{7}{5}\right)\)
\(=\dfrac{3}{4}\left(\dfrac{24}{15}+\dfrac{6}{15}-\dfrac{21}{15}\right)\)
\(=\dfrac{3}{4}.\dfrac{9}{15}\)
\(=\dfrac{9}{20}\)