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a) \(\frac{3^{17}.81^{11}}{27^{10}.9^{15}}=\frac{3^{17}.\left(3^4\right)^{11}}{\left(3^3\right)^{10}.\left(3^2\right)^{15}}=\frac{3^{17}.3^{44}}{3^{30}.3^{30}}=\frac{3^{61}}{3^{60}}=3\)
b) \(\frac{9^2.2^{11}}{16^2.6^3}=\frac{\left(3^2\right)^2.2^{11}}{\left(2^4\right)^2.2^3.3^3}=\frac{3^4.2^{11}}{2^8.2^3.3^3}=\frac{3^4.2^{11}}{2^{11}.3^3}=3\)
c) \(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2^{10}.3^{31}+2^{40}.3^6}{2.\left(2^{10}.3^{31}+2^{40}.3^6\right)}=\frac{1}{2}\)
\(A=\left|\frac{-1}{2}+\frac{1}{2}\right|-\left|\frac{-1}{2}+2\right|+\left|\frac{-1}{2}-\frac{3}{4}\right|\)\(\frac{3}{4}|\)
\(A=-\frac{3}{2}+\frac{5}{4}\)\(=\frac{-1}{4}\)
a: \(A=\left(\dfrac{15}{34}+\dfrac{9}{34}-1-\dfrac{15}{17}\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)
\(=\left(\dfrac{12}{17}-1-\dfrac{15}{17}\right)+1\)
\(=\dfrac{-20}{17}+1=\dfrac{-3}{17}\)
b: \(B=\dfrac{-5}{3}\cdot16\dfrac{2}{7}-\dfrac{-5}{3}\cdot28\dfrac{2}{7}\)
\(=\dfrac{-5}{3}\left(16+\dfrac{2}{7}-28-\dfrac{2}{7}\right)=\dfrac{-5}{3}\cdot\left(-12\right)=20\)
c: \(C=25\cdot\dfrac{-1}{27}+\dfrac{1}{5}-2\cdot\dfrac{1}{4}-\dfrac{1}{2}\)
\(=\dfrac{-25}{27}+\dfrac{1}{5}-1\)
\(=\dfrac{-125+27-135}{135}=\dfrac{-233}{135}\)
\(\left(2\sqrt{3}\right)^2-\left(3\sqrt{2}\right)^2+\left(4\sqrt{0,5}\right)^2-\left(\frac{1}{5}\sqrt{125}\right)^2\)
\(=2^2.3-3^2.2+4^2.0,5-5\)
\(=12-18+8-5\)
\(=-3\)
`A = (3/4 - 5/6) : [7/8 - (1/2 + 3/16)]`
`=> A = (9/12 - 10/12) : [7/8 - (8/16 + 3/16)]`
`=> A = (-1/12) : (7/8 -11/16)`
`=> A = (-1/12) :(14/17 - 11/16)`
`=> A = (-1/12) : 3/16`
`=> A = (-1)/12 xx 16/3`
`=> A = ((-1)*16)/(12*3) = -16/36 = -4/9`
Vậy `A = -4/9`
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