Tính hợp lý
(3/5)^10 * (5/3)^10 - 13^4/39^4 + 2017^0
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a) 10-11+12-13+14-15+...-2017+2018
=(10-11)+(12-13)+(14-15)+...+(2016-2017)+2018
=(-1)+(-1)+(-1)+...+(-1)+2018
=(-1).1004+2018
=-1004+2018
=1004
b) -5+6-7+8-9+10-...-2017+2018
=-5+(6-7)+(8-9)+...+(2016-2017)+2018
=(-5)+(-1)+(-1)+...+(-1)+2018
=(-5)+(-1).1006+2018
=(-5)+(-1006)+2018
=1007
c) 3-4+5-6+7-8+...+101-102+103
= (3-4)+(5-6)+(7-8)+...+(101-102)+103
= (-1)+(-1)+(-1)+...+(-1)+103
= (-1).50+103 = (-50)+103
= 53
a,\(\frac{7}{10}\cdot\frac{4}{9}+\frac{3}{10}\cdot\frac{4}{9}-1\frac{7}{9}\)
\(=\frac{14}{45}+\frac{2}{15}-\frac{16}{9}\)
\(=\frac{14}{45}+\frac{6}{45}-\frac{80}{45}\)
\(=\frac{-60}{45}=\frac{-4}{3}\)
b,\(\frac{-5}{6}+\frac{4}{9}\cdot\left(\frac{5}{4}-\frac{2}{3}\right)\cdot\left(-3\right)^2+\frac{5}{9}\cdot30\%\)
\(=\frac{-5}{6}+\frac{4}{9}\cdot\left(\frac{7}{12}\right)\cdot9+\frac{5}{9}\cdot\frac{3}{10}\)
\(=\frac{-5}{6}+\frac{7}{3}+\frac{1}{6}\)
\(=\frac{-5}{6}+\frac{14}{6}+\frac{1}{6}\)
=\(=\frac{10}{6}=\frac{5}{3}\)
\(\left(\frac{3}{5}\right)^{10}.\left(\frac{5}{3}\right)^{10}-\frac{13^4}{39^4}+2017^0\\ =\left(\frac{3}{5}.\frac{5}{3}\right)^{10}-\left(\frac{13}{39}\right)^4+1\\ =1^{10}-\left(\frac{1}{3}\right)^4+1\)
\(=1-\frac{1}{81}+1\\ =2+\frac{-1}{81}\\ =\frac{161}{81}\)
(3/5)^10.(5/3)^10-13^4/39^4+2017^0
=1-1/81+1
=161/81