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\(\frac{3^{10}+6^2}{5.3^8+20}\)\(=\frac{3^2+2^2.3^2}{5+2^2.5}=\frac{3^2\left(1+2^2\right)}{5\left(1+2^2\right)}\)\(=\frac{3^2}{5}\)\(=\frac{9}{5}\)
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\(\frac{5^2.6^9.10+6^5.2^3.15^3}{5^2.6^8.10-2.6^8.10^3}=\frac{5^2.2^9.3^9.2.5+2^5.3^5.2^3.5^3.3^3}{5^2.2^8.3^8.2.5-2.2^8.3^8.2^3.5^3}\)
\(=\frac{2^{10}.3^9.5^3+2^8.3^8.5^3}{2^9.3^8.5^3-2^{12}.3^8.5^3}=\frac{2^8.3^8.5^3\left(2^2.3+1\right)}{2^9.3^8.5^3\left(1-2^3\right)}\)
\(=\frac{13}{2.-7}=-\frac{13}{14}\)
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\(Q=\frac{2^{12}.3^5-4^6.81}{\left(2^2.3\right)^6+8^4.3^5}=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}\)
\(=\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}=\frac{2}{3.4}=\frac{1}{6}\)
Q = \(\frac{2^{12}.3^5-4^6.81}{\left(2^2.3\right)^6+8^4.3^5}\)
= \(\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}\)
= \(\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}\)
= \(\frac{2}{3.4}=\frac{1}{6}\)
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\(\frac{3^{10}+6^2}{5\cdot3^8+20}\)
\(=\frac{3^{10}+\left(3\cdot2\right)^2}{5\left(3^8+4\right)}\)
\(=\frac{3^{10}+3^2\cdot2^2}{5\left(3^8+4\right)}\)
\(=\frac{3^2\left(3^8+4\right)}{5\left(3^8+4\right)}\)
\(=\frac{9}{5}\)
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a: \(=\dfrac{2^4\cdot3^6\cdot2\cdot3}{2^4\cdot3^6}=6\)
b: \(=\dfrac{2^{20}\cdot3^{20}}{2^{18}\cdot3^{18}}=2^2\cdot3^2=36\)
c: \(=\dfrac{12^5\cdot13}{12^6\cdot13}-\dfrac{12^8\cdot\left(-11\right)}{12^9\cdot\left(-11\right)}=\dfrac{1}{12}-\dfrac{1}{12}=0\)
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\(\frac{2^5.3^6+6^5.11}{12^5-6^5.2^2}\)
\(=\frac{2^5.3^6+2^5.3^5.11}{2^2.3-2^5.3^5.2^2}\)
\(=\frac{2^5.3^5.\left(3+11\right)}{2^2.3\left(1-2^5.3^4\right)}\)
\(=\frac{2^3.3^4.14}{1-32.81}\)
\(=\frac{2^4.3^4.7}{-2591}\)
\(\frac{2^5\cdot3^6+6^5\cdot11}{12^5-6^5.2^2}\)
\(=\frac{6^5\cdot3+6^5\cdot11}{6^5\cdot2^5-6^5\cdot2^2}\)
\(=\frac{6^5\cdot\left(3+11\right)}{6^5\cdot\left(2^5-2^2\right)}\)
\(=\frac{14}{32-4}\)
\(=\frac{14}{28}=\frac{1}{2}\)