Mình rút gọn như sau:

   \(\frac{6^3+3.6^2+3^3}{-13}\)

\(=\frac{2^3.3^3+3.2^2.3^2+3^3}{-13}\)

\(=\frac{3^2.\left(2^3+3.2^2+3\right)}{-13}\)

\(=\frac{9.\left(8+12+3\right)}{-13}\)

\(=\frac{9.23}{-13}=\frac{207}{-13}\)

Vì tử số và mẫu số ko cùng chia hết cho 1 số nào ngoài 1 suy ra phân số trên tối giản

Bạn Dark Killer làm sai òi 

Ta có: \(\frac{6^3+3.6^2+3^3}{-13}=\frac{3^3.2^3+3.3^2.2^2+3^3}{-13}\)\(=\frac{3^3.\left(2^3+2^2+1\right)}{-13}=\frac{3^3.13}{-13}=3^3.\left(-1\right)=-27\)

n=10/7

o=27

(-10 phần 3 )³.(-6 phần 5)⁴

=-1000 phần 27.-1296 phần 625

=1296000 phần 16875 bạn tự giuts gọn nhé

2:(1 phần 2 - 2 phần 3)³

=2:(3 phần 6 - 4 phần 6 )³

=2:(-1 phần 6)³

2:-1 phần 216

=2.-216

=-432

6³+3.6²+3³ phần -13

=216+3 . 36+27 phần -13

216+108+27 phần -13

=351 phần -13

=-27

=

b) \(\frac{36^7}{2^{15}.27^5}=\frac{\left(2^2.3^2\right)^7}{2^{15}.\left(3^3\right)^5}=\frac{2^{14}.3^{14}}{2^{15}.3^{15}}=\frac{1.1}{2.3}=\frac{1}{6}\)

h) \(\frac{2^{18}.9^4}{6^6.8^4}=\frac{2^{18}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^4}=\frac{2^{18}.3^8}{2^6.3^6.2^{12}}=\frac{2^{18}.3^8}{2^{18}.3^6}=\frac{1.3^2}{1.1}=9\)

o) \(\frac{3^3+3.6^2+6^3}{13}=\frac{3^3+6^2\left(3+6\right)}{13}=\frac{3^3+6^2.3^2}{13}\)

\(=\frac{3^2\left(3+6^2\right)}{13}=\frac{9.3.13}{13}=\frac{9.3.1}{1}=27\)

\(a,=\frac{2^7\cdot\left(3^2\right)^3}{2^5\cdot3^5\cdot2^3}=\frac{2^7\cdot3^6}{2^8\cdot3^5}=\frac{3}{2}\)

câu a)

\(=\frac{2^7\times\left(3^2\right)^3}{2^5\times3^5\times2^3}=\frac{2^7\times3^6}{2^8\times3^5}=\frac{3}{2}\)

Bài làm

a) \(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{\left(2.3\right)^5.\left(2^3\right)^2}=\frac{2^7.3^5}{2^5.3^5.2^5}=\frac{1.1}{1.1.2^3}=\frac{1}{2^3}=\frac{1}{8}\)

b) \(\frac{6^3+3.6^2+3^3}{-13}=\frac{6^2.6+3.6^2+3^3}{-13}=\frac{6^2.\left(6+3+3^3\right)}{-13}=\frac{36.36}{-13}\approx-99,7\)

c) \(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(4.5\right)^4}{\left(5^2\right)^5.4^5}=\frac{5^4.4^4.5^4}{5^7.4^7}=\frac{5.1.1}{1.4^3}=\frac{5}{64}\approx0,08\)

# Chúc bạn học tốt #

a.

\(\frac{2^7\times9^3}{6^5\times8^2}=\frac{2^7\times\left(3^2\right)^3}{\left(2\times3\right)^5\times\left(2^3\right)^2}=\frac{2^7\times3^6}{2^5\times3^5\times2^6}=\frac{3}{2^4}=\frac{3}{16}\)

b.

\(\frac{6^3+3\times6^2+3^3}{-13}=\frac{\left(2\times3\right)^3+3\times\left(3\times2\right)^2+3^3}{-13}=\frac{2^3\times3^3+3\times3^2\times2^2+3^3}{-13}=\frac{8\times3^3+3^3\times4+3^3}{-13}\)\(=\frac{3^3\times\left(8+4+1\right)}{-13}=\frac{27\times13}{-13}=-27\)

c.

\(\frac{5^4\times20^4}{25^5\times4^5}=\frac{\left(5\times20\right)^4}{\left(25\times4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)

d.

\(\left(\frac{5^4-5^3}{125^4}\right)=\frac{5^3\times\left(5-1\right)}{\left(5^3\right)^4}=\frac{5^3\times4}{5^{12}}=\frac{4}{5^9}\)

a)\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}\)

b)\(\frac{6^3+3.6^2+3^3}{-13}=\frac{6.6^2+3.6^2+3^3}{-13}=\frac{6^2.\left(6+3\right)+3^3}{-13}=\frac{6^2.9+3^3}{-13}=\frac{6^2.3^2+3.3^2}{-13}=\frac{3^2.\left(6^2+3\right)}{-13}=\frac{3^2.39}{-13}=3^2.\left(-3\right)=-27\)

c)\(\frac{5^4.20^4}{25^5.4^5}=\frac{100^4}{100^5}=\frac{1}{100}\)

làm nhanh giùm mình nha mình đang cần gấp

a)  \(\frac{45^{10}.5^{20}}{75^{15}}=\frac{5^{10}.9^{10}.5^{20}}{5^{15}.5^{15}.3^{15}}=\frac{5^{30}.3^{20}}{5^{30}.3^{15}}=3^5=243\)

b) \(\frac{6^3+3.6^2+3^3}{-13}=\frac{2^3.3^3+3.2^2.3^2+3^3}{-13}\)

\(=\frac{3^3.\left(2^3+2^2+1\right)}{-13}=\frac{3^3.13}{-13}=-3^3=-27\)

c) \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.5}\)

\(=\frac{2.6}{3.5}=\frac{4}{5}\)

d) \(\frac{3.11+42}{5^3}=\frac{33+42}{5^3}=\frac{75}{5^3}=\frac{5^2.3}{5^3}=\frac{3}{5}\)

Câu a là 243

Câu b là -27

Câu c là 4 phần 5

câu d là 3 phần 5

a) \(\frac{2^7\cdot9^3}{6^5\cdot8^2}=\frac{2^7\cdot\left(3^2\right)^3}{\left(2\cdot3\right)^5\cdot\left(2^3\right)^2}=\frac{2^7\cdot3^6}{2^5\cdot3^5\cdot2^6}=\frac{3}{2^4}=\frac{3}{16}\)

c) \(\frac{5^4\cdot20^4}{25^4\cdot4^5}=\frac{5^4\cdot\left(2^2\cdot5\right)^4}{\left(5^2\right)^4\cdot\left(2^2\right)^5}=\frac{5^4\cdot2^8\cdot5^4}{5^8\cdot2^{10}}=\frac{1}{2^2}=\frac{1}{4}\)

d) \(\frac{\left(5^4\cdot20^4\right)^3}{125^4}=\frac{5^{12}\cdot20^{12}}{\left(5^3\right)^4}=\frac{5^{12}\cdot\left(2^2\cdot5\right)^{12}}{5^{12}}=2^{24}\cdot5^{12}\)

\(A=\frac{3}{2+\sqrt{3}}+\frac{13}{4-\sqrt{3}}+\frac{6}{\sqrt{3}}\)

\(=\frac{3\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}+\frac{13\left(4+\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}+\frac{6}{\sqrt{3}}\)

\(=6-3\sqrt{3}+4+\sqrt{3}+\frac{6}{\sqrt{3}}\)

\(=10-2\sqrt{3}+\frac{6}{\sqrt{3}}\)

\(=\frac{10\sqrt{3}-6+6\sqrt{3}}{\sqrt{3}}\)

\(=\frac{16\sqrt{3}-6}{\sqrt{3}}\)