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\(\frac{1}{3}\times x+\frac{3}{4}\times x-75\%=\frac{-21}{4}\)
a)\(=\frac{2017}{2016}.\frac{3}{4}-\frac{1}{2016}.\frac{3}{4}\)
\(=\frac{3}{4}\left(\frac{2017}{2016}-\frac{1}{2016}\right)\)
\(=\frac{3}{4}.1\)
\(=\frac{3}{4}\)
b)\(=\frac{2015}{2016}\left(\frac{1}{2}+\frac{1}{3}-\frac{5}{6}\right)\)
\(=\frac{2015}{2016}.0\)
\(=0\)
a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)
\(\left(3\frac{1}{2}+5\frac{2}{3}\right)\times\frac{8}{19}-\left(2\frac{1}{2}+4\frac{2}{3}\right)\times\frac{8}{19}\)
\(=\frac{8}{19}\times\left[\left(3\frac{1}{2}+5\frac{2}{3}\right)-\left(2\frac{1}{2}+4\frac{2}{3}\right)\right]\)
\(=\frac{8}{19}\times\left(3\frac{1}{2}+5\frac{2}{3}-2\frac{1}{2}-4\frac{2}{3}\right)\)
\(=\frac{8}{19}\times\left[\left(3\frac{1}{2}-2\frac{1}{2}\right)+\left(5\frac{2}{3}-4\frac{2}{3}\right)\right]\)
\(=\frac{8}{19}\times\left(1+1\right)\)
\(=\frac{8}{19}\times2=\frac{16}{19}\)
\(12\cdot5-\left(3x+1\right)=4-\left(-40\right)\)
\(\Leftrightarrow60-3x-1=44\)
\(\Leftrightarrow60-1-3x=44\)
\(\Leftrightarrow59-3x=44\)
\(\Leftrightarrow3x=59-44=15\)