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

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

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)\(=\frac{3^7}{2^2.3^4}=\frac{3^3}{2^2}=\frac{27}{4}\)

b)\(=\frac{2^{20}+2^{12}}{2^{10}+2^{18}}=\frac{2^{12}\left(2^8+1\right)}{2^{10}\left(1+2^8\right)}=\frac{2^{12}}{2^{10}}=2^2=4\)

-46/24 5

trình bày đày đủ giúp em ạ

\(a,\dfrac{5}{3}\times\dfrac{4}{5}=\dfrac{4}{3}\) (phần rút gọn : bỏ 5)

\(b,\dfrac{2}{3}\times\dfrac{3}{7}=\dfrac{2}{7}\) (phần rút gọn : bỏ 3)

\(c,\dfrac{7}{13}\times\dfrac{13}{7}=1\) (phần rút gọn : bỏ 7 và 13)

a)\(\dfrac{5}{3}\)x\(\dfrac{4}{5}\)=\(\dfrac{5x4}{3x5}\)=\(\dfrac{20}{15}\)=\(\dfrac{4}{3}\)(rút gọn \(\dfrac{20}{15}\)=\(\dfrac{4}{3}\))

b)\(\dfrac{2}{3}\)x\(\dfrac{3}{7}\)=\(\dfrac{2x3}{3x7}\)=\(\dfrac{6}{21}\)=\(\dfrac{2}{7}\)(rút gọn\(\dfrac{6}{21}\)=\(\dfrac{2}{7}\))

c)\(\dfrac{7}{13}\)x\(\dfrac{13}{7}\)=\(\dfrac{7x13}{13x7}\)=\(\dfrac{91}{91}\)=1(rút gọn\(\dfrac{91}{91}\)=1)

BÀI 1

\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{\left(2.3\right)^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}=\frac{3}{16}.\)

bài 2

a)           \(\frac{1}{2}-\frac{1}{3}+\frac{1}{12}=\frac{6}{12}-\frac{4}{12}+\frac{1}{12}=\frac{3}{12}=\frac{1}{4}\)

b)          \(\frac{9^9.27^4}{3^8.81^5}=\frac{\left(3^2\right)^9.\left(3^3\right)^4}{3^8.\left(3^4\right)^5}=\frac{3^{18}.3^{12}}{3^8.3^{20}}=\frac{3^{30}}{3^{28}}=3^2=9\)

Study well 

Bài 1: \(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}=\frac{3}{16}\)

Bài 2: 

a)\(\frac{1}{2}-\frac{1}{3}+\frac{1}{12}=\frac{6}{12}-\frac{4}{12}+\frac{1}{12}=\frac{6-4+1}{12}=\frac{1}{4}\)

b)\(\frac{9^9.27^4}{3^8.81^5}=\frac{9^9.3^{12}}{3^8.9^{10}}=\frac{3^4}{9}=\frac{3^4}{3^2}=3^2=9\)