Mai nộp rồi giúp với

\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}=\dfrac{3^6.3^85^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)

\(=\dfrac{3^{14}.5^4-3^{13}.5^4}{2.3^{12}.5^6}=\dfrac{3^{13}.5^4\left(3-1\right)}{2.3^{12}.5^6}\)

\(=\dfrac{3.2}{2.5^2}=\dfrac{3}{25}\)

a)

5⁷ . 25⁷ và 625⁵

Ta có:

5⁷ . 25⁷ = 125⁷ =( 5³ )⁷ = 5^3.7 = 5²¹

625⁵ = ( 5⁴ )⁵ =5^4.5 = 5²⁰

Vì 5²¹ > 5²⁰ => 5⁷ . 25⁷ > 625⁵

Vậy 5⁷ . 25⁷ > 625⁵

b) ( 3⁴ )⁴ và ( 3² )⁶

Ta có:

( 3⁴ )⁴ = 3^4.4 = 3¹⁶

( 3² )⁶ = 3^2.6 = 3¹²

Vì 3¹⁶ > 3¹² => ( 3⁴ )⁴ > ( 3² )⁶

Vậy  ( 3⁴ )⁴ > ( 3² )⁶

c) 8 . 2⁴ và 2⁹

Ta có:

8 . 2⁴ = 2³ . 2⁴ = 2⁷

Vì 2⁷ < 2⁹ => 8 . 2⁴ < 2⁹

Vậy 8 . 2⁴ < 2⁹

Học tốt!!!

\(=\dfrac{3^6\cdot3^{10}\cdot5^5-3^{13}\cdot5^{13}:5^9}{3^{12}\cdot5^6+5^6\cdot3^{12}}=\dfrac{3^{16}\cdot5^5-3^{13}\cdot5^4}{3^{12}\cdot5^6\cdot2}\)

\(=\dfrac{5^4\cdot3^{13}\left(3^3\cdot5-1\right)}{3^{12}\cdot5^6\cdot2}=\dfrac{3}{25}\cdot\dfrac{134}{2}=\dfrac{3}{25}\cdot67=\dfrac{201}{25}\)

\(=\dfrac{3^6\cdot3^8\cdot5^4-3^3\cdot5^3\cdot5^9}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{5^4\cdot3^3\cdot\left(3^{11}-5^8\right)}{3^{12}\cdot5^6\cdot2}=\dfrac{-106739}{3^9\cdot5^2}\)

\(=\dfrac{3^6\cdot\left(3^2\right)^4\cdot5^4-5^{13}\cdot3^{13}\cdot5^{-9}}{3^{12}\cdot5^6+\left(3^2\right)^6\cdot5^6}\)

\(=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{3^{13}\cdot5^4\cdot2}{2\cdot3^{12}\cdot5^6}=\dfrac{3}{5^2}=\dfrac{3}{25}\)

tử số=3^6.45^4-15^13.5^-9=3^6.(5.3^2)^4-(3.5)^13.5^-9=3^6.5^4.3^8-3^13.5^13.5^-9=3^14.5^4-3^13.5^4(3-1)=2.3^13.5^4

mẫu số=27^4.25^3+45^6=3^12.5^6+3^12.5^6=2.3^12.5^6

phân số =(2.3^13.5^4)/2.3^12.5^6=3/25

Bạn trinh bày rõ hơn đi

Kq thì ok rùi