Bài 1: Tính a) \(\left(\frac{11}{12}:\frac{44}{16}\right)\cdot\left(-\frac{1}{3}+\frac{1}{2}\right)\) b) \(\frac{\left(-5^2\right)\left(-5\right)^3\cdot16}{5^4\cdot\left(-2\right)^4}\) c) \(7,5:\left(\frac{-5}{3}\right)+2\frac{1}{2}:\left(\frac{-5}{3}\right)\) ...
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Bài 1: Tính a) \(\left(\frac{11}{12}:\frac{44}{16}\right)\cdot\left(-\frac{1}{3}+\frac{1}{2}\right)\) b) \(\frac{\left(-5^2\right)\left(-5\right)^3\cdot16}{5^4\cdot\left(-2\right)^4}\) c) \(7,5:\left(\frac{-5}{3}\right)+2\frac{1}{2}:\left(\frac{-5}{3}\right)\) d) \(\left|-\frac{3}{7}\right|:\left(-3\right)^2-\sqrt{\frac{4}{49}}\)
a) \(\left(\frac{11}{12}:\frac{44}{16}\right)\cdot\left(-\frac{1}{3}+\frac{1}{2}\right)=\left(\frac{11}{12}\cdot\frac{16}{44}\right)\cdot\frac{1}{6}=\left(\frac{1}{3}\cdot\frac{4}{4}\right)\cdot\frac{1}{6}=\frac{1}{3}\cdot\frac{1}{6}=\frac{1}{18}\)
b) \(\frac{\left(-5\right)^2\cdot\left(-5\right)^3\cdot16}{5^4\cdot\left(-2\right)^4}=\frac{5^2\cdot\left(-5\right)^3\cdot2^4}{5^4\cdot2^4}=\frac{5^2\cdot\left(-5\right)^3\cdot2^4}{5^2\cdot5^2\cdot2^4}=\frac{\left(-5\right)^3}{5^2}=-5\)
c) \(7,5:\left(-\frac{5}{3}\right)+2\frac{1}{2}:\left(-\frac{5}{3}\right)=7,5:\left(-\frac{5}{3}\right)+2,5:\left(-\frac{5}{3}\right)=\left(7,5+2,5\right):\left(-\frac{5}{3}\right)\)
\(=10:\left(-\frac{5}{3}\right)=10\cdot\left(-\frac{3}{5}\right)=-6\)
d) \(\left|-\frac{3}{7}\right|:\left(-3\right)^2-\sqrt{\frac{4}{49}}=\frac{3}{7}:9-\frac{2}{7}=\frac{3}{7}\cdot\frac{1}{9}-\frac{2}{7}=\frac{1}{7}\cdot\frac{1}{3}-\frac{2}{7}=\frac{1}{21}-\frac{2}{7}=-\frac{5}{21}\)