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\(\dfrac{-2^3\cdot3^3\cdot5^3\cdot7\cdot8}{3\cdot5^3\cdot2^4\cdot42}\)
\(=\dfrac{-2^6\cdot3^3\cdot5^3\cdot7}{3\cdot5^3\cdot2^4\cdot2\cdot3\cdot7}\)
\(=\dfrac{-2^6\cdot3^3\cdot5^3}{2^5\cdot3^2\cdot5^3}=-2\cdot3=-6\)
\(A=\frac{\left(-2\right)^3.3^3.5^3.7.8}{3.2^4.5^3.14}=\frac{\left(-8\right).3^2.3.5^3.7.8}{3.2^3.2.5^3.2.7}=\frac{\left(-8\right).9}{2.2}=\frac{-72}{4}=-18\)
\(\frac{2^5.7+2^5}{2^5.5^2-2^5.3}=\frac{2^5.\left(7+1\right)}{2^5.\left(5^2-3\right)}=\frac{8}{25-3}=\frac{8}{22}=\frac{4}{11}\)
\(\frac{3^4.5-3^6}{3^4.13+3^4}=\frac{3^4.\left(5-3^2\right)}{3^4.\left(13+1\right)}=\frac{5-9}{14}=\frac{-4}{14}=\frac{-2}{7}\)
\(\frac{-2}{7}=\frac{-22}{77}\)
\(\frac{4}{11}=\frac{28}{77}\)
\(\frac{\left(-2\right)^3.3^3.5^3.7.8}{3.2^4.5^3.14}=\frac{2^5.3^3.5^3.7.\left(-2\right)}{3.2^5.5^3.7}=\frac{3^2.\left(-2\right)}{1}=-18\)
\(P=\frac{3^9\cdot3^{20}\cdot2^8}{3^{24}\cdot243\cdot2^6}\)
\(P=\frac{3^{29}\cdot2^8}{3^{29}\cdot2^6}\)
\(P=2^2=4\)
\(Q=\frac{2^{15}\cdot5^3\cdot2^6\cdot3^4}{8\cdot2^{18}\cdot81\cdot5}\)
\(Q=\frac{2^{21}\cdot5^3\cdot3^4}{2^{21}\cdot3^4\cdot5}\)
\(Q=5^2=25\)
Ta có: \(\dfrac{3^4\cdot2^3-3^4\cdot4}{3^5\cdot3^2-3^5\cdot5}\)
\(=\dfrac{3^4\cdot\left(2^3-4\right)}{3^5\cdot\left(3^2-5\right)}\)
\(=\dfrac{3^4\cdot4}{3\cdot3^4\cdot4}=\dfrac{1}{3}\)
\(\dfrac{3^4\cdot2^3-3^{\text{4}}\cdot4}{3^5\cdot3^2-3^5\cdot5}\)=\(\dfrac{3^4\left(8-4\right)}{3^5\left(9-5\right)}\)=\(\dfrac{4}{3.4}\)=\(\dfrac{1}{4}\)