a) 2^3.3^3.5^3.7.8/ 3.2^4.5^3.14= 2^6 . 3^3 . 5^3 . 7/ 3. 2^5. 7. 5^3

rút gọn sau đó ra kết quả: 2. 3^2=18

b) 9. 5²⁰. 27⁹- 3.9¹⁵.25⁹/ 7.3²⁹. 125⁶- 3.3⁹. 15¹⁹= 3². 5²⁰- 3.3³⁰.5¹⁸/7.3²⁹.5¹⁸- 3¹⁰.3¹⁹.5¹⁹

=3². 5²⁰-3³¹.5¹⁸/ 7.3²⁹.5¹⁸ - 3²⁹.5¹⁹= 3². 5¹⁸ ( 25-3²⁹) / 3²⁹. 5¹⁸.2

tiếp theo em tu giai nhe

vâng em cảm ơn nhiều ạ !

`Answer:`

a. \(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}\)

\(=\frac{3^2.7.2.2.2}{2.7.2}\)

\(=\frac{3^2.2}{1}\)

\(=18\)

b. \(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)

Ta xét tử số: \(9.5^{20}.27^9-3.9^{15}.25^9\)

\(=3^2.5^{20}.\left(3^3\right)^9-3.\left(3^2\right)^{15}.\left(5^2\right)^9\)

\(=3^2.5^{20}.3^{27}-3.3^{30}.5^{18}\)

\(=5^{20}.3^{29}-3^{31}.5^{18}\)

\(=3^{29}.5^{18}.\left(5^2-3^2\right)\)

\(=3^{29}.5^{18}.16\)

Ta xét mẫu số: \(7.3^{29}.125^6-3.3^9.15^{19}\)

\(=7.3^{29}.\left(5^3\right)^6-3^{10}.\left(3.5\right)^{19}\)

\(=7.3^{29}.5^{18}-3^{10}.3^{19}.5^{19}\)

\(=7.3^{29}.5^{18}-3^{29}.5^{19}\)

\(=3^{29}.5^{18}.\left(7-5\right)\)

\(=3^{29}.5^{18}.2\)

`=>` Phân số trở thành: \(\frac{3^{29}.5^{18}.16}{3^{29}.5^{18}.2}\)\(=\frac{16}{2}=8\)

3².5²⁰.(3³)⁹-3.(3²)¹⁵.(5²)⁹

7.3²⁹.(5³)

\(=\dfrac{3^2\cdot5^{20}\cdot3^{27}-3\cdot3^{30}\cdot5^{18}}{7\cdot3^{29}\cdot5^{13}-3^{29}\cdot5^{19}}=\dfrac{3^{29}\cdot5^{20}-5^{18}\cdot3^{31}}{3^{29}\cdot5^{13}\cdot7-3^{29}\cdot5^{19}}\)

\(=\dfrac{3^{29}\cdot5^{18}\left(5^2-3^2\right)}{3^{29}\cdot5^{13}\left(7-5^6\right)}=5^5\cdot\dfrac{4^2}{7-5^6}\)

bt cách lm rùi còn j 

\(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)

\(=\frac{3^2.5^{20}.3^{27}-3.3^{30}.5^{18}}{7.3^{29}.5^{18}-3^{10}.3^{19}.5^{19}}\)

\(=\frac{3^{29}.5^{18}.5^2-3^2.3^{29}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{18}.5}\)

\(=\frac{3^{29}.5^{18}.\left(5^2-3^2\right)}{3^{29}.5^{18}.\left(7-5\right)}\)

\(=\frac{25-9}{2}\)

\(=\frac{16}{2}=8\)

                                                       Bài giải

\(N=\frac{9\cdot5^{20}\cdot27^9-3\cdot9^{15}\cdot25^9}{7\cdot3^{29}\cdot125^6-3\cdot3^9\cdot15^{19}}=\frac{3^2\cdot5^{20}\cdot\left(3^3\right)^9-3\cdot\left(3^2\right)^{15}\cdot\left(5^2\right)^9}{7\cdot3^{29}\cdot\left(5^3\right)^6-3\cdot3^9\cdot\left(3\cdot5\right)^{19}}=\frac{3^2\cdot5^{20}\cdot3^{27}-3\cdot3^{30}\cdot5^{18}}{7\cdot3^{29}\cdot5^{18}-3^{10}\cdot3^{19}\cdot5^{19}}\)

\(=\frac{3^{29}\cdot5^{20}-3^{31}\cdot5^{18}}{7\cdot3^{29}\cdot5^{18}-3^{29}\cdot5^{19}}=\frac{3^{29}\cdot5^{18}\left(5^2-3^2\right)}{3^{29}\cdot5^{18}\left(7-5\right)}=\frac{25-9}{7-5}=\frac{16}{2}=8\)

1. \(\dfrac{9.5^{20}.27^9-3.9^{15}:25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)

\(=\dfrac{3^2.5^{20}.3^{27}-3.3^{30}.5^{18}}{7.3^{29}.5^{18}-3^{10}.3^{19}.5^{19}}\)

\(=\dfrac{3^{29}.5^{20}-3^{31}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{19}}\)

\(=\dfrac{3^{28}.5^{18}.\left(5^2-3^2\right)}{3^{29}.5^{18}.\left(7-5\right)}\)

\(=\dfrac{5^2-3^2}{7-5}=\dfrac{16}{2}=8\)

2.\(\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{-4}\right)^{20}=\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{4}\right)^{20}\)

\(=\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{2}^2\right)^{20}=\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{2}\right)^{40}\)

\(=\left(\dfrac{1}{2}\right)^{55}\)

3.\(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\dfrac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)

\(=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}=\dfrac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}\)

\(=\dfrac{1-3}{1+5}=\dfrac{-2}{6}=\dfrac{-1}{3}\)

Chúc học tốt!!