5⁵-5⁴+5³=5³.(5²-5¹+5⁰)=5³.(25-5+1)=5³.21=5³.3.7 chia hết cho 7

=>ĐPCM

7⁶+7⁵-7⁴=7⁴.(7²+7¹-7⁰)=7⁴.(49+7-1)=7⁴.55=7⁴.5.11 chia hết cho 11

=>ĐPCM

\(S=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{11}\left(1+2\right)=3\left(2+2^3+...+2^{11}\right)⋮3\)

\(S=2\left(1+2+2^2\right)+...+2^{10}\left(1+2+2^2\right)=7\left(2+...+2^{10}\right)⋮7\)

Vì S chia hết cho 2 và S chia hết cho 3 

nên \(S⋮6\)

\(\overline{aaa}+\overline{bbb}=111.a+111.b=111\left(a+b\right)=37\times3\times\left(a+b\right)⋮37\)

\(3.\overline{abcabc}-605=3.\left(1000\overline{abc}+\overline{abc}\right)-605=3.1001.\overline{abc}-695=11\left(273\overline{abc}-55\right)⋮11\)

\(\overline{abc}+\overline{bca}+\overline{cab}=\left(100a+10b+c\right)+\left(100b+10c+a\right)+\left(100c+10a+b\right)\)

\(=111\left(a+b+c\right)=37\times3\times\left(a+b+c\right)⋮37\)

1)Đưa về lũy thừa cùng cơ số 2

8²=  \(\left(2^3\right)^2=2^6\)        32³= \(\left(2^5\right)^3=2^{15}\)          64⁴= \(\left(2^6\right)^4=2^{24}\)       4³= \(\left(2^2\right)^{^3}=2^6\)

2)Đưa về lũy thừa cùng cơ số 3

9³= \(\left(3^2\right)^3=3^6\)       27⁴=  \(\left(3^3\right)^4=3^{12}\)      9⁵= \(\left(3^2\right)^5=3^{10}\)      81⁶=   \(\left(3^4\right)^6=3^{24}\)

3)Đưa về lũy thừa cùng cơ số 2

 8³:4²= \(\left(2^3\right)^3:\left(2^2\right)^2=2^9:2^4=2^5\)    16²:32= \(\left(2^4\right)^2:2^5=2^8:2^5=2^3\)    

\(64^4:4^3=\left(2^6\right)^4:\left(2^2\right)^3=2^{24}:2^6=2^{18}\)    32³:8²= \(\left(2^5\right)^3:\left(2^3\right)^2=2^{15}:2^6=2^9\)

Bạn giải nốt hộ mình câu 4,,5,6 mình cảm ơn nhìu

4)Đưa về lũy thừa cùng cơ số 3

27⁴:9³=\(\left(3^3\right)^4:\left(3^2\right)^3=3^{12}:3^6=3^6\)    81^6:9⁵=  \(\left(3^4\right)^6:\left(3^2\right)^5=3^{24}:3^{10}=3^{14}\)   

9⁶ .27⁴:81⁵=\(\left(3^2\right)^6.\left(3^3\right)^4:\left(3^4\right)^5=3^{12}.3^{12}:3^{20}=3^4\)

5)Đưa về lũy thừa cùng cơ số 5

25⁷=  \(\left(5^2\right)^7=5^{14}\)    125³=  \(\left(5^3\right)^3=5^9\)   25⁷:5⁶=  \(\left(5^2\right)^7:5^6=5^{14}:5^6=5^8\)

125⁶:25⁷= \(\left(5^3\right)^6:\left(5^2\right)^7=5^{18}:5^{14}=5^4\)

6)Đưa về lũy thừa cùng cơ số 4

16²= \(\left(4^2\right)^2=4^4\)     64³=\(\left(4^3\right)^3=4^9\)      (128:2)³=\(64^3=\left(4^3\right)^3=4^9\)     2².2²=\(4.4=4^2\)

a: \(=\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\cdot\dfrac{-7}{11}=-\dfrac{5}{11}\)

b: \(=\dfrac{12}{7}\left(19+\dfrac{5}{8}-15-\dfrac{1}{4}\right)=\dfrac{12}{7}\cdot\left(4+\dfrac{3}{8}\right)\)

\(=\dfrac{12}{7}\cdot\dfrac{35}{8}=\dfrac{3}{2}\cdot5=\dfrac{15}{2}\)

c: \(=\dfrac{2}{15}-\dfrac{2}{15}\cdot5+\dfrac{3}{15}=\dfrac{2}{15}\cdot\left(-4\right)+\dfrac{3}{15}=\dfrac{-8+3}{15}=\dfrac{-5}{15}=-\dfrac{1}{3}\)

d: \(=\dfrac{4}{9}\left(19+\dfrac{1}{3}-39-\dfrac{1}{3}\right)=\dfrac{4}{9}\cdot\left(-20\right)=-\dfrac{80}{9}\)