1. \(\frac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}=\frac{3^{10}\left(11+5\right)}{3^9\cdot2^4}=\frac{3^{10}\cdot2^4}{3^9\cdot2^4}=3\)

2. \(\frac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}=\frac{2^{10}\cdot\left(13+65\right)}{2^8\cdot104}=\frac{2^{10}\cdot78}{2^8\cdot104}=\frac{2^8\cdot2^2\cdot2\cdot3\cdot13}{2^8\cdot2^3\cdot13}=\frac{2^8\cdot2^3\cdot3\cdot13}{2^8\cdot2^3\cdot13}=3\)

3. \(\frac{72^2\cdot54^2}{108^4}=\frac{\left(2^3\cdot3^2\right)^2\cdot\left(2\cdot3^3\right)^2}{\left(2^2\cdot3^3\right)^4}\)

\(=\frac{2^6\cdot3^4\cdot2^2\cdot3^6}{2^8\cdot3^{12}}=\frac{2^8\cdot3^{10}}{2^8\cdot3^{12}}=\frac{3^{10}}{3^{12}}=3^{-2}=\frac{1}{9}\)

4. \(\frac{21^2\cdot14\cdot125}{35^5\cdot6}=\frac{\left(3\cdot7\right)^2\cdot2\cdot7\cdot5^3}{\left(5\cdot7\right)^5\cdot2\cdot3}=\frac{3^2\cdot7^2\cdot2\cdot7\cdot5^3}{5^5\cdot7^5\cdot2\cdot3}=\frac{3^2\cdot7^3\cdot2\cdot5^3}{5^3\cdot5^2\cdot7^2\cdot7^3\cdot2\cdot3}=\frac{3^2}{5^2\cdot3\cdot7^2}=\frac{3}{1225}\)

\(A=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}=\frac{3^{10}.16}{3^9.16}=3\)

\(B=\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.78}{2^8.104}=\frac{2^{10}.26.3}{2^8.2^2.26}=3\)

\(C=\frac{72^3.52^4}{108^4}=\frac{\left(3^2.2^3\right)^3.\left(13.2^2\right)^4}{\left(3^3.2^2\right)^4}=\frac{3^6.2^9.13^4.2^8}{3^{12}.2^8}=\frac{2^9.13^4}{3^6}\)

\(D=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}=\frac{11.3^{29}-3^{30}}{2^2.3^{28}}=\frac{3^{29}\left(33-1\right)}{2^2.3^{28}}=\frac{3^{29}.2^5}{2^2.3^{28}}=3.8=24\)

Bạn tách từng bài ra cho mọi người dễ làm nhé.

@ Hữu Nghĩa

bn í tách r mà!

\(\frac{3^{10}.11+3^{10}.10}{3^9.2^4}\)

\(=\frac{3^{10}.\left(11+10\right)}{3^9.2^4}=\frac{3^{10}.21}{3^9.16}\)

\(=\frac{3.21}{16}=\frac{63}{16}\)

Bài giải.

\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}=\frac{3^{10}.(11+5)}{3^9.2^4}=\frac{3.16}{2^4}=\frac{3.2^4}{2^4}=3\)

_Học tốt_

\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)

\(=\frac{3^{10}.\left(11+5\right)}{3^9.2^4}=\frac{3^{10}.16}{3^9.16}\)

\(=\frac{3^{10}}{3^9}=3\)

3^10.11 + 3^10.5 : ( 3^9.2^4)

=3^10.(11+5) : (3^9.2^4)

=(3^10.16) : (3^9.16)

=3^10 : 3^9

=3

Có gì sai thì góp ý cho mình nhé, Tks ! :)))

A) 4¹⁰ . 8¹⁵ = (2²)¹⁰ . (2³)¹⁵ = 2²⁰ . 2⁴⁵ = 2²⁰⁺⁴⁵=2⁶⁵

B) 4¹⁵ . 5³⁰ = (2²)¹⁵ . 5³⁰ = 2³⁰ . 5³⁰ = (2 . 5)³⁰ = 10³⁰

C) 27¹⁶ : 9¹⁰ = (3³)¹⁶ : (3²)¹⁰ = 3⁴⁸ : 3²⁰ =  3^48-20=3²⁸

20²-15².3[5²+22+2022⁰

1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)

b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)

c) \(10^8\div10^3=10^{8-3}=10^5\)

d) \(a^7\div a^2=a^{7-2}=a^5\)

2.

\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)

\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)

\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)

còn bài 2

a) 5³.25²:5⁴
= 5³.(5²)²:5⁴
= 5³.5⁴:5⁴
= 5^3+4-4
= 5³
b) 4².(2³)²:128
= (2²)².2⁶:2⁷
= 2⁴.2⁶:2⁷
= 2^4+6-7
= 2³
c) 3⁵.243:(3²)³
= 3⁵.3⁵:3⁶
= 3^5+5-6
= 3⁴
d) 20⁵:5⁵
= (20:5)⁵
= 4⁵
e) 4¹⁰:8¹⁰ (Có chắc không vậy ? Hay là 8¹⁰:4¹⁰ ?)
g) 4¹⁵.5³⁰
= 4¹⁵.(5²)¹⁵
= 4¹⁵.25¹⁵
= (4.25)¹⁵
= 100¹⁵
h) 27¹⁶.9¹⁰
= (3³)¹⁶.(3²)¹⁰
= 3⁴⁸.3²⁰
= 3⁴⁸⁺²⁰
= 3⁶⁸

Ko biết đúng hay sai nhưng cũng căm ơn bạn  nameless nha