ta có tử =45³x20⁴x18²=45x45x45x20x20x20x20x18x18

                                 =45x45x45x4x5x4x5x4x5x4x5x18x18

                                 =(45x4x45x4x45x4)x4x5x5x5x5x18x18

                                 =(180x180x180)x4x5x5x5x5x9x2x9x2

                                 =(180x180x180)x(4x5x9x2x2x5x9)x5x5

                                 =(180x180x180x180x180)x25

                                 =180⁵x25

lại có:180mũ5x25:180mux5=25

H= 45^3.20^4.18^2/ 180^5 = (3^2.5)^3.(2^2.5)^4.(2.3^2)^2/ (2^2.3^2.5)^5 = 3^6.5^3.2^8.5^4.2^2.3^4/ 2^10.3^10.5^5 = 3^10.5^7.2^10/ 2^10.3^10.5^5 = 5^2=25

G=(21².14.125):35⁵.6

=\(\frac{\left(3.7\right)^2.7.2.5^{^3}}{\left(7.5\right)^5.2.3}\)=\(\frac{3^2.7^2.7.5^3}{7^5.5^5.3}\)=\(\frac{3}{7^2.5^2}\)=\(\frac{3}{49.25}\)=\(\frac{3}{1225}\)

\(G=\frac{21^2.14.125}{35^5.6}\)

\(G=\frac{\left(3.7\right)^2.7.2.5^3}{\left(7.5\right)^5.2.3}=\frac{3}{7^2.5^2}=\frac{3}{49.25}=\frac{3}{1225}\)

bn biết làm phần H k

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

\(C=\frac{21^2.14.125}{35^3.6}\)

\(C=\frac{\left(3.7\right)^2.2.7.5^3}{\left(5.7\right)^3.2.3}\)

\(C=\frac{3^2.7^2.2.7.5^3}{5^3.7^3.2.3}\)

\(C=\frac{3^2.7^3.2.5^3}{5^3.7^3.2.3}=3\)

\(D=\frac{45^3.20^4.18^2}{180^5}\)

\(D=\frac{\left(5.3^2\right)^3.\left(2^2.5\right)^4.\left(2.3^2\right)^2}{\left(2^2.3^2.5\right)^5}\)

\(D=\frac{5^3.3^6.2^8.5^4.2^2.3^4}{2^{10}.3^{10}.5^5}\)

\(D=\frac{5^7.3^{10}.2^{10}}{2^{10}.3^{10}.5^5}=5^2=25\)

ti ck mik nhá

\(\frac{21^2\cdot14\cdot125}{35^2\cdot6}=\frac{3^2\cdot7^2\cdot2\cdot25\cdot3}{5^2\cdot7^2\cdot2\cdot3}=\frac{3^4\cdot7^2\cdot2\cdot5^2}{5^2\cdot7^2\cdot2\cdot3}=3^3=27..\)

\(\frac{45^3\cdot20^4\cdot18^2}{180^5}=\frac{5^3\cdot9^3\cdot4^4\cdot5^4\cdot2^2\cdot9^2}{2^{10}\cdot3^{10}\cdot5^5}=\frac{5^7\cdot9^5\cdot4^4}{4^5\cdot9^5\cdot5^5}=\frac{1}{4}=0.25\)

1)   = 7*3*2*7*5*5*5/7*5*7*5*2*3

câu 2 tt

d) Ta có: \(D=\dfrac{21^2\cdot14\cdot125}{35^3\cdot6}\)

\(=\dfrac{7^2\cdot3^2\cdot7\cdot2\cdot5^3}{5^3\cdot7^3\cdot6}\)

\(=\dfrac{3^2\cdot2}{6}=\dfrac{6\cdot3}{6}=3\)

e) Ta có: \(E=\dfrac{45^3\cdot20^4\cdot18^2}{180^5}\)

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

\(=\dfrac{3^{10}\cdot5^7\cdot2^{10}}{2^{10}\cdot3^{10}\cdot5^5}=25\)

f) Ta có: \(F=\dfrac{2^{13}+2^5}{2^{10}+2^2}\)

\(=\dfrac{2^5\left(2^8+1\right)}{2^2\left(2^8+1\right)}=\dfrac{2^5}{2^2}=\dfrac{32}{4}=8\)

c

Giải:

\(D=\dfrac{21^2.14.125}{35^3.6}\) 

\(D=\dfrac{\left(3.7\right)^2.\left(2.7\right).5^3}{\left(5.7\right)^3.\left(2.3\right)}\) 

\(D=\dfrac{3^2.7^2.2.7.5^3}{5^3.7^3.2.3}\) 

\(D=\dfrac{3^2.7^3.2.5^3}{5^3.7^3.2.3}\) 

\(D=3\) 

\(E=\dfrac{45^3.20^4.18^2}{180^5}\) 

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

\(E=\dfrac{\left(3^2\right)^3.5^3.\left(2^2\right)^4.5^4.2^2.\left(3^2\right)^2}{\left(2^2\right)^5.\left(3^2\right)^5.5^5}\) 

\(E=\dfrac{3^6.5^7.2^8.2^2.3^4}{2^{10}.3^{10}.5^5}\) 

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

\(E=5^2=25\) 

\(F=\dfrac{2^{13}+2^5}{2^{10}+2^2}\) 

\(F=\dfrac{2^2.2^3.2^8+2^2.2^3}{2^2.2^8+2^2}\) 

\(F=\dfrac{2^2.2^3\left(2^8+1\right)}{2^2.\left(2^8+1\right)}\) 

\(F=2^3=8\) 

Bài này lúc đầu mk cx ko thành thạo về bài này nên mk thấy khó nhưng sau đó mk luyện bài này nên đã lm quên vs bài này rồi!

Mk gợi ý lm bài này nha:

Nếu là nhân hay chia mk phải phân tích ra thừa số 

Nếu là cộng hay trừ mk phải tách ra sao cho nó có thể tính nhanh

Đấy là cách lm của mk!

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

45³ = (9.5)³ = 3⁶.5³

20⁴ = (4.5)⁴ = 2⁸.5⁴

18² = (9.2)² = 3⁴.2²

180⁵ = (4.9.5)⁵ = 2¹⁰.3¹⁰.5⁵

\(=\dfrac{3^6.5^3.2^8.5^4.3^4.2^2}{2^{10}.3^{10}.5^5}=\dfrac{2^{10}.3^{10}.5^7}{2^{10}.3^{10}.5^5}=5^2=25\)

\(B=\dfrac{11.3^{29}-3^{30}}{4.3^{28}}=\dfrac{3^{29}\left(11-3\right)}{3^{28}.4}=\dfrac{3.8}{4}=6\)