\(9^7+81^4-27^5\)

\(=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\)

\(=3^{14}+3^{16}-3^{15}\)

\(=3^{14}.\left(1+3^2-3\right)\)

\(=3^{14}.7⋮7\)

=> đpcm

\(25^{25}+5^{49}-125^{16}\)

\(=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\)

\(=5^{50}+5^{49}-5^{48}\)

\(=5^{48}.\left(5^2+5-1\right)\)

\(=5^{48}.29⋮29\)

=> đpcm

              Bài làm :

\(\text{1) }9^7+81^4-27^5\)

\(=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\)

\(=3^{14}+3^{16}-3^{15}\)

\(=3^{14}\left(1+3^2-3\right)\)

\(=3^{14}.7⋮7\)

=> Điều phải chứng minh

\(\text{2)}25^{25}+5^{49}-125^{16}\)

\(=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\)

\(=5^{50}+5^{49}-5^{48}\)

\(=5^{48}\left(5^2+5-1\right)\)

\(=5^{48}.29⋮29\)

=> Điều phải chứng minh

a. 

\(9^7+81^4-27^5\) 

\(=\left(3^2\right)^7+\left(3^4\right)^4-\left(3^3\right)^5\) 

\(=3^{14}+3^{16}-3^{15}\) 

\(=3^{14}\left(1+3^2-3\right)\) 

\(=3^{14}\left(1+9-3\right)\) 

\(=3^{14}\cdot7⋮7\left(đpcm\right)\) 

b. 

\(25^{25}+5^{49}-125^{16}\) 

\(=\left(5^2\right)^{25}+5^{49}-\left(5^3\right)^{16}\) 

\(=5^{50}+5^{49}-5^{48}\) 

\(=5^{48}\left(5^2+5-1\right)\) 

\(=5^{48}\left(25+5-1\right)\) 

\(=5^{48}\cdot29⋮29\left(đpcm\right)\)

a, 4¹⁰. 2³⁰=2²⁰.2³⁰=2⁵⁰

b,9²⁵.27⁴.81³= 3⁵⁰.3¹².3¹²=3⁷⁴

Tương tự các câu khác....

a, 4¹⁰.2³⁰ = (2²)¹⁰.2³⁰ = 2²⁰.2³⁰ = 2⁵⁰
b, 9²⁵.27⁴.81³ = (3²)²⁵.(3³)⁴.(3⁴)³ = 3⁵⁰.3¹².3¹² = 3⁷⁴
c, 25⁵⁰.125⁵ = (5²)⁵⁰.(5³)⁵ = 5¹⁰⁰.5¹⁵ = 5¹¹⁵
d, 64³.4⁸.16⁴ = (2⁶)³.(2²)⁸.(2⁴)⁴ = 2¹⁸.2¹⁶.2¹⁶ = 2⁵⁰
e, 3⁸ : 3⁶ = 3²
2¹⁰ : 8³ = 2¹⁰ : (2³)³ = 2¹⁰ : 2⁹ = 2
12⁷ : 6⁷ = (12 : 6)⁷ = 2⁷
@Dương Tuyết Mai

2^40 nha bạn. Chắc chắn 100%

a/ A = 2.2².2³.2⁴.2⁸ = 2¹⁸

b/ B = 3.3².3³.3⁴.3⁶ = 3¹⁶

c/ C = 2.5².5³.5⁴.5⁷ = 2.5¹⁶

d/ D = 7.7².7³.7⁷ = 7¹³

1) \(125^5:25^7\)

\(=\left(5^3\right)^5:\left(5^2\right)^7\)

\(=5^{15}:5^{14}\)

= 5

2) \(27^8:9^9\)

\(=\left(3^3\right)^8:\left(3^2\right)^9\)

\(=3^{24}:3^{18}\)

\(=3^6\)

3) \(36^5:6^8\)

\(=\left(6^2\right)^5:6^8\)

\(=6^{10}:6^8\)

\(=6^2\)

4) \(49^6:7^{10}\)

\(=\left(7^2\right)^6:7^{10}\)

\(=7^{12}:7^{10}=7^2\)

5) \(7^{20}:49^9\)

\(=7^{20}:\left(7^2\right)^9\)

\(=7^{20}:7^{18}=7^2\)

6) \(\frac{1}{2^{10}}:\frac{1}{8^3}\)

\(=\frac{1}{2^{10}}:\frac{1}{\left(2^3\right)^3}\)

\(=\frac{1}{2^{10}}:\frac{1}{2^9}=\frac{1}{2^{10}}.\frac{2^9}{1}=\frac{1}{2}\)

7) \(\left(-\frac{1}{2}\right)^{21}:\frac{1}{4^{10}}\)

\(=\frac{\left(-1\right)^{21}}{2^{21}}:\frac{1}{\left(2^2\right)^{10}}\)

\(=-\frac{1}{2^{21}}:\frac{1}{2^{20}}=-\frac{1}{2^{21}}.\frac{2^{20}}{1}\)

\(=-\frac{1}{2}\)

8) \(\frac{1}{16^5}:\left(-\frac{1}{2}\right)^{18}\)

\(=\frac{1}{\left(2^4\right)^5}:\frac{\left(-1\right)^{18}}{2^{18}}\)

\(=\frac{1}{2^{20}}:\frac{1}{2^{18}}\)

\(=\frac{1}{2^{20}}.\frac{2^{18}}{1}=\frac{1}{4}\)

9) \(\frac{1}{5^{30}}:\frac{1}{25^{14}}\)

\(=\frac{1}{5^{30}}:\frac{1}{\left(5^2\right)^{14}}\)

\(=\frac{1}{5^{30}}:\frac{1}{5^{28}}=\frac{1}{25}\)

1/2×(2×x-3)+105/2=-137/2

1/2×(2×x-3)=-137/2-105/2

1/2×(2×x-3)=-242/2

2×x-3=-242/2:1/2

2×x-3=-242

2.x=(-242)+3

2.x=239

x=239:2

x=239/2

A,-12×25-25×75-25×13

=[(-12)-75-13].25

=(-100).25

-2500

B,-50/7×49/10-35/2×-10/7+ -25/3× -9/5

=(-35)-(-25)+(-13)

=-23

C,-354+265-156+125

=[(-354)-156]+(265+125)

=(-510)+277

=-233

D,-74+40-50+16-35

=(-74)+40+(-50)+16+(-35)

=[(-74)+(-35)]+[40+(-50)+16]

=(-109)+26

=-83

E,-2/3×4/5+-4/5×4/3-0,125

=-2/3.4/5+4/5.(-4/3)-0,125

=4/5.[-2/3+(-4/3)]-0,125

=4/5.(-2)-0,125

=-8/5-0,125

=(-1,6)+(-0,125)

=-1,725

bai toán này kho lắm

tớ cũng đanh thắc mắc câu này

\(a,\dfrac{5^{16}\cdot27^7}{125^5\cdot9^{11}}=\dfrac{5^{16}\cdot\left(3^3\right)^7}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}\)

\(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)

\(b,\left(-0,2\right)^2\cdot5-\dfrac{2^{13}\cdot27^3}{4^6\cdot9^5}\)

\(=0,04\cdot5-\dfrac{2^{13}\cdot\left(3^3\right)^3}{\left(2^2\right)^6\cdot\left(3^2\right)^5}\)

\(=0,2-\dfrac{2^{13}\cdot3^9}{2^{12}\cdot3^{10}}\)

\(=0,2-\dfrac{2}{3}\)

\(=-\dfrac{7}{15}\)

\(c,\dfrac{5^6+2^2\cdot25^3+2^3\cdot125^2}{26\cdot5^6}\)

\(=\dfrac{5^6+2^2\cdot\left(5^2\right)^3+2^3\cdot\left(5^3\right)^2}{5^6\cdot26}\)

\(=\dfrac{5^6+4\cdot5^6+8\cdot5^6}{5^6\cdot26}\)

\(=\dfrac{5^6\left(1+4+8\right)}{5^6\cdot26}\)

\(=\dfrac{13}{26}\)

\(=\dfrac{1}{2}\)

#\(Toru\)

\(a,\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{\left(5^2\right)^8.9^7.3^7}{25^5.5^5.9^{11}}\\ =\dfrac{25^8.9^7.\left(3^2\right)^3.3}{25^5.\left(5^2\right)^2.5.9^{11}}=\dfrac{25^8.9^7.9^3.3}{25^5.25^2.5.9^{11}}\\ =\dfrac{25^8.9^{10}.3}{25^7.5.9^{11}}=\dfrac{25^7.9^{10}.25.3}{25^7.9^{10}.5.9}\\ =\dfrac{25.3}{5.9}=\dfrac{5.5.3}{5.3.3}=\dfrac{5}{3}\)

1: 8=2^3

2: 25=5^2

3: 4=2^2

4: 49=7^2

5: 81=9^2

6: 36=6^2

7: 100=10^2

8: 121=11^2

9: 144=12^2

10: 169=13^2

11: 27=3^3

12: 125=5^3

13: 1000=10^3

14: 32=2^5

15: 243=3^5

16: 343=7^3

17: 216=6^3

18: 64=4^3

19: 225=15^2

20: 128=2^7