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\(a,\dfrac{2^4.6^7}{9^3.4^6}=\dfrac{2^4.\left(2.3\right)^7}{\left(3^2\right)^3.\left(2^2\right)^6}=\dfrac{2^4.2^7.3^7}{3^6.2^{12}}=\dfrac{2^{11}.3^7}{3^6.2^{12}}=\dfrac{3}{2}\)
\(b,\dfrac{3^{18}.24^4}{9^4.81^5}=\dfrac{3^{18}.\left(3.2^3\right)^4}{\left(3^2\right)^4.\left(3^4\right)^5}=\dfrac{3^{18}.3^4.2^{12}}{3^8.3^{20}}=\dfrac{3^{22}.2^{12}}{3^{28}}=\dfrac{2^{12}}{3^8}\)

a: \(=\left(1+\dfrac{4}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}\)
\(=1+1+\dfrac{1}{2}=2+\dfrac{1}{2}=\dfrac{5}{2}\)
b: \(=\left(\dfrac{1}{25}+\dfrac{5}{25}+\dfrac{25}{25}\right):\left(\dfrac{1}{25}-\dfrac{5}{25}-\dfrac{25}{25}\right)\)
\(=\dfrac{31}{25}:\dfrac{-29}{25}=\dfrac{-31}{29}\)
c: \(=\dfrac{\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}}{\dfrac{4}{9}-\dfrac{4}{7}-\dfrac{4}{11}}+\dfrac{\dfrac{3}{5}-\dfrac{3}{25}-\dfrac{3}{125}-\dfrac{3}{625}}{\dfrac{4}{5}-\dfrac{4}{25}-\dfrac{4}{125}-\dfrac{4}{625}}\)
=1/4+3/4
=1
`-5/7*2/11+9/7*(-5)/11+5/7`
`=-5/7*2/11+(-5)/7*9/11+5/7`
`=(-5/7)*2/11+(-5)/7*9/11+(-5/7)*(-1)`
`=(-5)/7*(2/11+9/11-1)`
`=(-5)/7*(11/11-1)`
`=(-5)/7*(1-1)`
`=(-5)/7*0`
`=0`
\(-\frac57.\frac{2}{11}+\frac97.\left(-\frac{5}{11}\right)+\frac57\)
\(=-\frac{10}{77}-\frac{45}{77}+\frac57\)
\(=-\frac{10}{77}-\frac{45}{77}+\frac{55}{77}\)
\(=\frac{-10-45+55}{77}\)
\(=\frac{0}{77}\)
\(=0\)