​​\(\frac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\)

=\(\frac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}\)

=\(\frac{11\cdot3^{29}-3^{29}\cdot3}{2^2\cdot3^{28}}\)

=\(\frac{3^{29}\cdot\left(11-3\right)}{2^2\cdot3^{28}}\)

=\(\frac{3^{29}\cdot2^3}{2^2\cdot3^{28}}\)

=\(\frac{3\cdot2}{1}\)

=6

tách mẫu ra: (2.3¹⁴)² = 2².(3¹⁴)² nha

duyệt đi

A=(11.3^22.3^7-9^15)/ ( 2.3^14)
=(11.3^29-3^30) /(2.3^14)
=[3^29(11-3) / (2.3^14]
=(3^29.8) / (2.3^14)
=(3^29:3^14) /(8:2)
=3^15/4

\(\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)

\(=\frac{11.3^{29}-3^{30}}{2^2.3^{28}}\)

\(=\frac{3^{29}.\left(11-3\right)}{2^2.3^{28}}\)

\(=\frac{3^{29}.2^3}{2^2.3^{28}}\)

\(=3.2=6\)

\(A=\frac{3^7\cdot17-3^9}{2^3\cdot3^5}=\frac{3^7\left(17-3^2\right)}{2^3\cdot3^5}=\frac{3^7\cdot2^3}{2^3\cdot3^5}=9\)

\(B=\frac{3^2\cdot4^2\cdot2^{32}}{11\cdot2^{13}\cdot4^{11}-16^9}=\frac{3^2\cdot2^{36}}{2^{35}\cdot11-2^{36}}=\frac{3^2\cdot2^{36}}{2^{35}\left(11-2\right)}=\frac{3^2\cdot2^{36}}{2^{35}\cdot3^2}=2\)

\(\frac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}=\frac{3^{29}\left(11-3\right)}{2^2\cdot3^{28}}=\frac{3^{29}\cdot8}{2^2\cdot3^{28}}=6\)

\(C=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}-3^{30}}{4.3^{28}}=\frac{3^{29}\left(11-3\right)}{4.3^{28}}=\frac{3.8}{4}=6\)

                                                    Bài giải

a, \(\frac{7}{12}+\frac{5}{6}+\frac{1}{4}-\frac{3}{7}-\frac{5}{12}\)

\(=\left(\frac{7}{12}-\frac{5}{12}+\frac{5}{6}+\frac{1}{4}\right)-\frac{3}{7}=\left(\frac{7}{12}-\frac{5}{12}+\frac{10}{12}+\frac{3}{12}\right)-\frac{3}{7}=\frac{5}{4}-\frac{3}{7}=\frac{23}{28}\)

b, \(\frac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}=\frac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}=\frac{3^{29}\left(11-3\right)}{3^{28}\cdot4}=\frac{3\cdot8}{4}=6\)

-29 

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làm cụ thể ra hộ mình

\(\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}+7.2^{29}.3^{18}}\)

\(=\frac{5.2^{18}.3^{18}.2^{12}-2.2^{28}.3^{14}.3^4}{2^{28}.3^{18}.\left(5+7.2\right)}\)

\(=\frac{5.2^{30}.3^{18}-2^{29}.3^{18}}{2^{28}.3^{18}.19}=\frac{2^{28}.3^{18}.\left(5.4-2\right)}{2^{28}.3^{18}.19}\)

\(=\frac{5.4-2}{19}=\frac{18}{19}\)

ta có \(\frac{5\left(2^2.3^2\right)^9.\left(2^2\right)^6-\left(2^2.3\right)^{14}.9^{14}}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)

\(=\frac{5.2^{18}.3^{18}.2^{12}-2^{28}.3^{14}.3^8}{2^{28}.3^{18}\left(5.1.1-7.2.1\right)}\)

\(=\frac{2^{28}.3^{18}\left(5.1.3.2^2-1.3^4\right)}{2^{28}.3^{18}\left(5-14\right)}\)

\(=\frac{60-81}{5-14}=\frac{7}{3}\)