\(A=5^{61}+25^{31}+125^{21}\)

\(\Rightarrow A=5^{61}+\left(5^2\right)^{31}+\left(5^3\right)^{21}\)

\(\Rightarrow A=5^{61}+5^{62}+5^{63}\)

\(\Rightarrow A=5^{61}\left(1+5+5^2\right)\)

\(\Rightarrow A=5^{61}.31⋮31\)

\(\Rightarrow A⋮31\)

Vậy \(A⋮31\)

\(A=5^{61}+25^{31}+125^{21}\)

\(A=5^{61}+\left(5^2\right)^{31}+\left(5^3\right)^{21}\)

\(A=5^{61}+5^{62}+5^{63}\)

\(A=5^{61}\left(1+5+5^2\right)\)

\(A=5^{61}\cdot31⋮31\left(đpcm\right)\)

a) 600000

c) -40

e) 1922

b) -35

d) 350

b) \(\left(x-\dfrac{3}{5}\right)^2=4\)

\(\Leftrightarrow\sqrt{\left(x-\dfrac{5}{3}\right)^2}=\sqrt{4}\)

\(\Leftrightarrow\left|x-\dfrac{3}{5}\right|=2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{5}=2\\x-\dfrac{3}{5}=-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{13}{5}\\x=-\dfrac{7}{5}\end{matrix}\right.\)

vậy

a) \(5^{61}+\left(5^2\right)^{31}+\left(5^3\right)^{21}\)

\(5^{61}+5^{61}+5^{63}\)

\(5^{61}\left(1+5+5^2\right)\)

\(5^{61}.31⋮31\)

vậy....

5^61 + 25^31 + 125^21

= 5^61 + 5^62 + 5^63

= 5^61 x (1+5+25) 

= 5^61 x 31 chia hết 31

5^61 + 25^31 + 125^21

= 5^61 + 5^62 + 5^63

= 5^61 x (1+5+25) 

= 5^61 x 31 chia hết 31

\(5^{61}+25^{31}+125^{21}=5^{61}+5^{62}+5^{63}\)

                                         \(=5^{61}\left(1+5+5^2\right)=5^{61}.31\)

Chia het cho 31

a ) \(5^{61}+25^{31}+125^{21}=5^{61}+5^{62}+5^{63}=5^{61}\left(1+5+25\right)=5^{61}.31⋮31\)(đpcm)

b ) \(6^3+2.6^2+3^3=2^3.3^3+2^3.3^2+3^3=3^2\left(8.3+8+3\right)=3^2.35⋮35\) (đpcm)

Vậy ........

Cảm ơn các bạn nhiều lắm nha!!!

5^61+25^31+125^21 =5^61+5^62+5^63 =5^61(1+5+5^2) =5^61.31

Không chia hết cho 3 đâu bạn, chỉ 31 thôi

31x72 - 31x70 - 31 x 2 - 31

=31x(72 -70 -2 -1)

=31 x (-1)

= -31

những câu sau thì lam tương tự nha bạn ^_^

1) $(-35)\cdot18+28\cdot35$

$=35\cdot(-18)+28\cdot35$

$=35\cdot(-18+28)$

$=35\cdot10$

$=350$

2) $53\cdot29-47\cdot(-29)$

$=53\cdot29-47\cdot(-1)\cdot29$

$=53\cdot29+47\cdot29$

$=29\cdot(53+47)$

$=29\cdot100$

$=2900$

3) $125\cdot(-24)+24\cdot225$

$=(-125)\cdot24+24\cdot225$

$=24\cdot(-125+225)$

$=24\cdot100$

$=2400$

4) $26\cdot(-121)-121\cdot(-36)$

$=-121\cdot[26+(-36)]$

$=-121\cdot(26-36)$

$=-121\cdot(-10)$

$=121\cdot10$

$=1210$

5) $65\cdot(-25)+25\cdot(-23)$

$=-65\cdot25+25\cdot(-23)$

$=25\cdot(-65-23)$

$=25\cdot(-88)$

$=-2200$

6) $237\cdot(-26)+26\cdot137$

$=-237\cdot26+26\cdot137$

$=26\cdot(-237+137)$

$=26\cdot(-100)$

$=-2600$

7) $30\cdot(-125)+25\cdot30$

$=30\cdot(-125+25)$

$=30\cdot(-100)$

$=-3000$

8) $(-37)\cdot69+(-31)\cdot37$

$=37\cdot(-69)+37\cdot(-31)$

$=37\cdot(-69-31)$

$=37\cdot(-100)$

$=-3700$

9) $31\cdot72-31\cdot70-31\cdot2$

$=31\cdot(72-70-2)$

$=31\cdot(2-2)$

$=31\cdot0$

$=0$

10) $(-12)\cdot47+(-12)\cdot52+(-12)$

$=-12\cdot(47+52+1)$

$=-12\cdot100$

$=-1200$

$\text{#}Toru$