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\(\frac{5^4\cdot7^3\cdot a^5\cdot b^6}{5^3\cdot7a^3\cdot b^5}\)
\(=\frac{5^4}{5^3}\cdot\frac{7^3}{7}\cdot\frac{a^5}{a^3}\cdot\frac{b^6}{b^5}\)
\(=5\cdot7^2\cdot a^2\cdot b=245a^2b\)
1; 73.52.54.76:(55.78)
= (73.76).(52.54) : (55.78)
= 79.56: (55.78)
= (79:78).(56:55)
= 7.5
= 35
2; 33.a7.3.a2:(34.a6)
= (33.3).(a7.a2): (34.a6)
= 34.a9: (34.a6)
= (34:34).(a9:a6)
= a3
\(a,\)\(\frac{2^5\times3^{12}\times7^8}{2^7\times3^{10}\times7^9}=\frac{3^2\times\left(2^5\times3^{10}\times7^8\right)}{2^2\times7\times\left(2^5\times3^{10}\times7^8\right)}\)\(=\frac{3^2}{2^2\times7}=\frac{9}{28}\)
\(b,\)Tương tự
$\textbf{a)}$
$\dfrac{2^5\cdot3^{12}\cdot7^8}{2^7\cdot3^{10}\cdot7^9}$
$=\dfrac{3^{12-10}}{2^{7-5}\cdot7^{9-8}}$
$=\dfrac{3^2}{2^2\cdot7}$
$=\dfrac{9}{28}.$
\(a,3^6:3^5=3^{6-5}=3\\ b,5^7:5^5=5^{7-5}=5^2=25\\ c,14^5:2^3:7^4=\left(2^5:2^3\right)\cdot\left(7^5:7^4\right)=2^2\cdot7=28\\ d,5^4-2\cdot5^3=5^3\left(5-2\right)=3\cdot5^3=375\)
a) 3^6 : 3^5 = 729 : 243 = 3
b) 5^7 : 5^5 = 78125 : 3125 = 25
c) 14^5 : 2^3 : 7^4 = 537824 : 8 : 2401 = 89
d) 5^4 - 2 * 5^3 = 625 - 2 * 125 = 625 - 250 = 375
\(a,3^6:3^5=3^{6-5}=3^1=3\\ b,5^7:5^5=5^{7-5}=5^2=25\\ c,14^5:2^3:7^4=\left(2^5:2^3\right).\left(7^5:7^4\right)=2^{5-3}.7^{5-4}=2^2.7^1=4.7=28\\ d,5^4-2.5^3=5.5^3-2.5^3=\left(5-2\right).5^3=3.5^3=3.125=375\)
$\textbf{A)}$
$\dfrac{2^{10}-2^7\cdot9}{2^7-2^4\cdot9}$
$=\dfrac{2^7(2^3-9)}{2^4(2^3-9)}$
$=\dfrac{2^7}{2^4}$
$=2^3$
$=8.$
$\textbf{B)}$
$\left(\dfrac{27^4}{9^5}+\dfrac{625^3}{125^4}\right)-2^3$
$=\left(\dfrac{(3^3)^4}{(3^2)^5}+\dfrac{(5^4)^3}{(5^3)^4}\right)-8$
$=(3^{12-10}+5^{12-12})-8$
$=(3^2+1)-8$
$=10-8$
$=2.$
a)\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{-5}{9}\)
b)\(\frac{\left(-11\right)^5.13^7}{11^5.13^8}=-\frac{1}{13}\)
c)\(\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3-1\right)}{2^9.3^{10}}=2\)
d(\(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(35+9\right)}=\frac{1}{6}\)
\(\frac{2^5\cdot3^7\cdot a^4\cdot b^3}{2^2\cdot3\cdot a^2b}\)
\(=\frac{2^5}{2^2}\cdot\frac{3^7}{3}\cdot\frac{a^4}{a^2}\cdot\frac{b^3}{b}\)
\(=2^3\cdot3^6\cdot a^2b^2=5832a^2b^2\)