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\(\frac{2^9.3^{10}+2^8.3^7.135}{2^{10}.3^{10}+2^9.3^{11}}\)\(=\frac{2^9.3^{10}+2^8.3^7.3^3.5}{2^{10}.3^{10}+2^9.3^{11}}=\frac{2^9.3^{10}+2^8.3^{10}.5}{2^{10}.3^{10}+2^9.3^{11}}=\frac{2^8.3^{10}.\left(2+5\right)}{2^8.3^{10}.\left(2^2+2.3\right)}=\frac{7}{10}\)
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\(=\frac{2^9.3^{10}+2^8.3^7.3^3.5}{2^{10}.3^{10}+2^9.3^{11}}=\frac{2^8.3^{10}.\left(2+5\right)}{2^8.3^{10}.\left(2^2+2.3\right)}=\frac{7}{10}\)
\(\dfrac{1}{9}.3^4.3^n=9^4\)
\(\dfrac{1}{9}.3^{4+n}=9^4\)
\(3^{4+n}=\dfrac{9^4}{\dfrac{1}{9}}\)
=> \(3^{4+n}=9^4.9\)
=> \(3^{4+n}=9^5\)
=> \(3^{4+n}=(3^2)^5\)
=> \(3^{4+n_{ }}=3^{10}\)
=> \(4+n=10\)
\(n=10-4\)
\(n=6\)
`(2^9 .3^11)/(4^5 .9^6)`
`=(2^9 .3^11)/((2^2)^5 .(3^2)^6)`
`=(2^9 .3^11)/(2^10 .3^12)`
`=1/(2.3)=1/6`
a,\(\dfrac{2^9.3^{11}}{4^5.9^6}=\dfrac{2^9.3^{11}}{2^{10}.3^{12}}=\dfrac{1}{2.3}=\dfrac{1}{6}\)
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