\(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}=\frac{2^3.3^3.5^3.7.2^3}{3.2^4.5^3.2.7}\)

\(=\frac{2^6.3^3.5^3.7}{2^5.3.5^3.7}=\frac{2.3^2.1.1}{1.1.1.1}=2.3^2\)

\(=2.9=18\)

\(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}=\frac{1.3^2.1.1.8}{1.2.1.2}=\frac{3.3.4}{2.1}=\frac{3.3.2}{1}=18\)

\(...=\frac{2^6.3^3.5^3.7}{2.^53.5^3.7}=18\)

\(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}\)mk viết như vầy bn cố gắng hiểu nhé:.

2³.3³.5³.7.8/ 3.2⁴.5³.14

= 2³.3³.5³.7.8/3.2⁴.5³.7.2

=2³.3³.5³.8/3.2⁴.5³.2

=2³.3³.5³.2³/2⁴.2.5³

= 2³.2³.3³.5³/ 2⁴.2.5³

= 2⁶. 3³.5³/ 2⁵. 5³

= 2⁵.2.3³.5³/2⁵.5³

= 2.3³/1

^{= 2. 27/1}

^{= 54/1 = 54}

^{Thế nha bn, chúc bn học tốt!}

a) \(\dfrac{2^4\cdot5^2\cdot7}{2^3\cdot5\cdot7^2\cdot11}=\dfrac{2^3\cdot5\cdot10\cdot7}{2^3\cdot5\cdot7\cdot77}=\dfrac{10}{77}\)

\(\dfrac{2^3\cdot3^3\cdot5^3\cdot7\cdot8}{3\cdot2^4\cdot5^3\cdot14}=\dfrac{2^3\cdot3\cdot5^3\cdot7\cdot3^2\cdot8}{3\cdot2^3\cdot2\cdot5^3\cdot14}=\dfrac{7\cdot3^2\cdot8}{2\cdot14}=\dfrac{63\cdot8}{2\cdot14}=18=\dfrac{1386}{77}\)

rút gọn rồi quy đồng nha

\(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}=\frac{2^6.3^3.5^3.7}{2^5.7.5^3.3}=\frac{2^5.3.5^3.7.\left(2.3^2\right)}{2^5.3.5^3.7}=18\)

=\(\frac{2^3.3^3.8}{3.2^4.2}\)

=\(\frac{2^3.3^3.4}{3.2^4}\)

=\(\frac{3^2.4}{2}\)

=\(3^2.2\)

=9.2

=18

Ta có:

\(\frac{\left(-2\right)^3.3^3.5^3.7.8}{3.5^3.2^4.42}=\frac{\left(-2\right).\left(-2\right).\left(-2\right).3.3.3.5.5.5.7.2.2.2}{3.5.5.5.2.2.2.2.2.3.7}\)

\(=\frac{\left(-2\right)}{1}=-2\)

bn ghi ro hơn ko 

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: \(\frac{3^{29}.5^{18}.16}{3^{29}.5^{18}.2}\)\(=\frac{16}{2}=8\)