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a, \(\dfrac{4^2.4^3}{2^{10}}=\dfrac{4^5}{2^{10}}=\dfrac{\left(2^2\right)^5}{2^{10}}=\dfrac{2^{10}}{2^{10}}=1\)
b, \(\dfrac{2^7.9^3}{6^5.8^2}=\dfrac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\dfrac{2^7.3^6}{2^5.3^5.2^6}=\dfrac{3}{2^4}=\dfrac{3}{16}\)
c, \(\dfrac{9^7.5^6.125^9}{15^{15}.5^{18}}=\dfrac{3^{21}.5^6.5^{27}}{5^{15}.3^{15}.5^{18}}=\dfrac{3^{21}.5^{33}}{3^{15}.5^{33}}=3^6=729\)
d, \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^9.\left(1+3.5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2.16}{3^2.5}=\dfrac{32}{45}\)
Chúc bạn học tốt!!!

\(a,\left[2^{17}+16^2\right]\cdot\left[9^{15}-3^{15}\right]\cdot\left[2^4-4^2\right]\)
\(=\left[2^{17}+16^2\right]\cdot\left[9^{15}-3^{15}\right]\cdot\left[16-16\right]\)
\(=\left[2^{17}+16^2\right]\left[9^{15}-3^{15}\right]\cdot0=0\)
\(b,\left[8^{2017}-8^{2015}\right]\cdot\left[8^{2014}\cdot8\right]\)
\(=8^{2015}\left[8^2-1\right]\cdot8^{2015}\)
\(=8^{2015}\cdot63\cdot8^{2015}=8^{4030}\cdot63\)sửa lại câu b , có vấn đề rồi
\(c,\frac{2^8+8^3}{2^5\cdot2^3}=\frac{2^8+\left[2^3\right]^3}{2^5\cdot2^3}=\frac{2^8+2^9}{2^8}=\frac{2^8\left[1+2\right]}{2^8}=3\)
2.a, \(2^6=\left[2^3\right]^2=8^2\)
Mà 8 = 8 nên 82 = 82 hay 26 = 82
b, \(5^3=5\cdot5\cdot5=125\)
\(3^5=3\cdot3\cdot3\cdot3\cdot3=243\)
Mà 125 < 243 nên 53 < 35
c, 26 = [23 ]2 = 82
Mà 8 > 6 nên 82 > 62 hay 26 > 62
d, 7200 = [72 ]100 = 49100
6300 = \(\left[6^3\right]^{100}\)= 216100
Mà 49 < 216 nên 49100 < 216100 hay 7200 < 6300

Năm nay mình mới lên lp 4 nên không biết làm bài này.
Xin bạn thông cảm.

94 . 86 / 610. 163
= (32)4 . (23)8 / ( 3.2)10 . (24)3
=38 . 224 / 310 . 210 . 212
= 22 / 32
= 4 / 9
= 0.(4)
Chúc bạn học tốt nhé!!!!
94 . 86 / 610 . 163
= 38 . 218 / 320 . 212
= 1. 26 / 312 . 1
Tự làm tiếp nha bạn!

\(B=\dfrac{9^3}{3^6.4}\)\(=\dfrac{\left(3^2\right)^3}{3^6.4}=\dfrac{3^6}{3^6.4}=\dfrac{1}{4}\)
\(C=\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\dfrac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2^2.5}=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}=\dfrac{\left(2^{10}.3^8\right)\left(1-3\right)}{\left(2^{10}.3^8\right)\left(1+5\right)}=\dfrac{-2}{6}=\dfrac{-1}{3}\)
\(D=\frac{2^{16}\cdot9^4}{6^6\cdot8^3}\)
\(=\frac{2^{16}\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^6\cdot\left(2^3\right)^3}\)
\(=\frac{2^{16}\cdot3^8}{2^6\cdot3^6\cdot2^9}\)
\(=\frac{2^{16}\cdot3^8}{3^6\cdot2^{15}}\)
\(=\frac{2\cdot3^2}{1\cdot1}\)
\(=2\cdot9=18\)
\(D=\frac{2^{16}\cdot9^4}{6^6\cdot8^3}\)
\(=\frac{2^{16}\cdot3^8}{\left(2\cdot3\right)^6\cdot2^9}\)
\(=\frac{2^{16}\cdot3^8}{2^{15}\cdot3^6}\)
\(=2\cdot3^2\)
\(=18\)