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a)\(A=\frac{5.2^{13}.2^{22}-2^{36}}{\left(3.2^{17}\right)^2}\)
\(A=\frac{5.2^{35}-2^{36}}{3^2.2^{34}}\)
\(A=\frac{2^{35}\left(5-2\right)}{3^2.2^{34}}\)
\(A=\frac{2.3}{3^2}=\frac{2}{3}\)
b) \(B=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)
\(B=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(B=\frac{2^{18}.3^9\left(2+5\right)}{2^{19}.3^9\left(2+3\right)}\)
\(B=\frac{7}{2.5}=\frac{7}{10}\)
\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}.....\frac{899}{30^2}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{29.31}{30.30}=\frac{1.2.3.....29}{2.3.4.....30}.\frac{3.4.5.....31}{2.3.4.....30}\)
\(=\frac{1}{2}.\frac{31}{30}=\frac{31}{60}\)
\(A=-1-4=-5\)
\(B=\frac{4}{3}.\frac{15}{7}-16\)
\(B=\frac{20}{7}-16\)
\(B=\frac{-92}{7}\)
\(C=\frac{28}{15}.0,25.3+\left(\frac{8}{15}-\frac{1}{4}\right)\div1\frac{23}{24}\)
\(C=1,4+\frac{17}{60}\div\frac{47}{24}\)
\(C=1,4+\frac{34}{235}\)
\(C=\frac{363}{235}\)
\(A=\frac{-15}{8}+\frac{7}{8}-4\)
\(=-1-4=-5\)
\(B=\left(4-2\frac{2}{3}\right).2\frac{1}{7}-1\frac{3}{5}:\frac{1}{10}\)
\(=\frac{4}{3}.\frac{15}{7}-\frac{8}{5}:\frac{1}{10}\)
\(=\frac{20}{7}-16=\frac{-92}{7}\)
\(C=1\frac{13}{15}.\left(0,5\right)^2.3+\left(\frac{8}{15}-25\%\right):1\frac{23}{24}\)
\(=\frac{28}{15}.\frac{1}{4}.3+\frac{17}{60}:\frac{47}{24}\)
\(=\frac{7}{15}.3+\frac{17}{60}:\frac{47}{24}\)
\(=\frac{7}{5}+\frac{34}{235}=\frac{363}{235}\)
2: \(=\dfrac{59}{10}\cdot\dfrac{2}{3}-\left[\dfrac{7}{3}\cdot\left(4+\dfrac{1}{2}-2\right)\right]\cdot\dfrac{4}{7}\)
\(=\dfrac{59}{15}-\dfrac{4}{3}\cdot\dfrac{5}{2}=\dfrac{59}{15}-\dfrac{10}{3}=\dfrac{59-50}{15}=\dfrac{9}{15}=\dfrac{3}{5}\)
4: \(=254+254\cdot399+399\)
\(=254\cdot400+399\)
\(=101600+399=101999\)
5: \(=638+3900-41=3900+597=4497\)
\(D=\frac{4^7.2^8}{3.2^{15}.16^2+5.2.\left(2^{10}\right)^2}\)
\(=\frac{2^{14}.2^8}{3.2^{15}.2^8+5.2.2^{20}}\)
\(=\frac{2^{22}}{3.2^{23}+5.2^{21}}\)
\(=\frac{2^{22}}{2^{21}.\left(2^2.3+5\right)}\)
\(=\frac{2}{2^2.3+5}\)
\(=\frac{2}{17}\)
\(D=\frac{\left(2^2\right)^7.2^8}{3.2^{15}.\left(2^4\right)^2+5.2^2.2^{20}}\)
\(=\frac{2^{14}.2^8}{3.2^{15}.2^8+5.2^{22}}\)
\(=\frac{2^{22}}{3.2^{23}+5.2^{22}}\)
\(=\frac{2^{22}}{2^{22}\left(3.2+5\right)}=\frac{1}{11}\)