\(\dfrac{2^2\cdot3^3\cdot5}{3\cdot2^3\cdot5^3}=\dfrac{1}{2}\cdot3^2\cdot\dfrac{1}{5^2}=\dfrac{1}{2}\cdot\dfrac{9}{25}=\dfrac{9}{50}\)

Giải:

a) \(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}\) 

\(=\dfrac{5^3.5.3^2.2.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}\) 

\(=\dfrac{5^4.3^2.2.2^6}{5^4.3^2.2^{13}}\) 

\(=\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}\) 

\(=\dfrac{1}{2^6}=\dfrac{1}{64}\) 

b) \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\) 

\(=\dfrac{15^2.16^3.16-15^2.16^3.15}{12^2.20^2.20-20^2.12^2.12}\) 

\(=\dfrac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}\) 

\(=\dfrac{\left(3.5\right)^2.\left(2^4\right)^3.1}{\left(3.2^2\right)^2.\left(2^2.5\right)^2.8}\) 

\(=\dfrac{3^2.5^2.2^{12}}{3^2.\left(2^2\right)^2.\left(2^2\right)^2.5^2.2^3}\) 

\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^4.2^4.2^3}\) 

\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^{11}}\) 

\(=2\) 

c) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\) 

\(=\dfrac{2.3+2.3.2.2+2.3.7.7}{3.5+3.5.2.2+3.5.7.7}\) 

\(=\dfrac{2.3+2.3.4+2.3.49}{3.5+3.5.4+3.5.49}\) 

\(=\dfrac{2.3.\left(1+4+49\right)}{3.5.\left(1+4+49\right)}\) 

\(=\dfrac{2.3}{3.5}\) 

\(=\dfrac{2}{5}\) 

Chúc bạn học tốt!

a: \(=\dfrac{2^{12}\cdot3^{14}}{3^{12}\cdot2^{12}}=3^2=9\)

b: \(=\dfrac{7^3\cdot2\cdot5^3}{5^2\cdot7^2\cdot6}=7\cdot5\cdot\dfrac{1}{3}=\dfrac{35}{3}\)

d: =2^5(2^8+1)/2^2(2^8+1)=2^3=8

c: \(=\dfrac{5^3\cdot3^6\cdot2^8\cdot5^4\cdot3^4\cdot2^2}{2^{10}\cdot3^{10}\cdot5^5}=5^2\)

Bạn ơi mik ra \(\dfrac{x^3+45x-54}{12\left(x-3\right)\left(x+3\right)}\) có đúng không bạn?

A = \(\dfrac{72^3.5^{42}}{108^4}\)

= \(\dfrac{\left(2^3.3^2\right)^3.5^{42}}{\left(2^2.3^3\right)^4}\)

= \(\dfrac{2^9.3^6.5^{42}}{2^8.3^{12}}\)

= \(\dfrac{2.5^{42}}{3^6}\)

@trần phúc nguyên

B = \(\dfrac{45^3.20^4.18^2}{180^5}\)

= \(\dfrac{\left(3^2.5\right)^3\left(2^2.5\right)^4.\left(2.3^2\right)^2}{\left(2^2.3^2.5\right)^5}\)

= \(\dfrac{3^6.5^3.2^8.5^4.2^2.3^4}{2^{10}.3^{10}.5^5}\)

= \(\dfrac{3^{10}.5^7.2^{10}}{2^{10}.3^{10}.5^5}\)

= 25
@trần phúc nguyên

C = \(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)

= \(\dfrac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}\)

= \(\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\)

= \(\dfrac{3^{29}\left(11-3\right)}{2^2.3^{28}}\)

= \(\dfrac{33-9}{4}\)

= 6
@trần phúc nguyên