Bài 1:

a, \(64^2=\left(2^6\right)^2=2^{12}\)

\(32^5=\left(2^5\right)^5=2^{25}\)

\(2^{12}< 2^{25}\Rightarrow64^2< 32^5\)

b, \(10^5=\left(5.2\right)^5=5^5.2^5\)

\(5^{10}=5^{5+5}=5^5.5^5\)

\(5^5.2^5< 5^5.5^5\Rightarrow10^5< 5^{10}\)

c, 256^ mấy thế hả bạn?

d, \(9^{200}=\left(9^2\right)^{100}=81^{100}\)

\(81^{100}>10^{100}\Rightarrow9^{200}>10^{100}\)

Bài 2:

\(9.27^2.81^3.216\)

\(=3^2.\left(3^3\right)^2.\left(3^4\right)^3.2^3.3^3\)

\(=3^2.3^6.3^{12}.3^3.2^3\)

\(=3^{2+6+12+3}.2^3\)

\(=3^{23}.2^3\)

a, Ta có :

\(\left(\frac{1}{2}\right)^{50}=\left(\left(\frac{1}{2}\right)^5\right)^{10}=\left(\frac{1}{32}\right)^{10}\)

bạn so sánh nha :)

b,

T/c : \(99^{20}=\left(\left(99\right)^2\right)^{10}=9801^{10}\)

tiếp đây thì bạn tự làm nha có gì k hiểu ibx mk

Ta có: \(199^{20}=\left(199^4\right)^5=1568239201^5\)

\(2003^{15}=\left(2003^3\right)^5=8036054027^5\)

Vì \(8036054027^5>1568239201^5\) nên \(2003^{15}>199^{20}\)

Ta có :

199²⁰ < 216²⁰ = ( 6³ )²⁰ = 6⁶⁰

2003¹⁵ > 1296¹⁵ = ( 6⁴ )¹⁵ = 6⁶⁰

Vì 199²⁰ < 6⁶⁰ < 2003¹⁵

=> 199²⁰ < 2003¹⁵ 

a)12/5<5/2

b)6/15>3/8

c)\(\frac{17}{18}<\frac{18}{19}\)

d) \(\frac{24}{23}\) < \(\frac{23}{22}\)

\(\dfrac{13}{17}< \dfrac{30}{34}\)                                        \(\dfrac{9}{8}>\dfrac{5}{7}\) 

 \(\dfrac{15}{7}< \dfrac{8}{3}\)                                        \(\dfrac{5}{7}< \dfrac{7}{5}\)                     

\(\dfrac{16}{20}=\dfrac{4}{5}\)

Bài 1: \(\frac{2}{3}^6\)

Bài 2: \(2^{24}< 3^{16}\)

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

\(1111=1000+100+10+1=10^3+10^2+10^1+1\)

\(1247=1000+2\times100+4\times10+7=10^3+2\times10^2+4\times10^1+7\)

\(1543=1000+5\times100+4\times10+3=10^3+5\times10^2+4\times10^1+3\)

\(1794=1000+7\times100+9\times10+4=10^3+7\times10^2+9\times10^1+4\)

\(1876=1000+8\times100+7\times10+6=10^3+8\times10^2+7\times10^1+6\)

\(1008=1000+8=10^3+8\)

\(1080=1000+8\times10=10^3+8\times10^1\)

\(1709=1000+7\times100+9=10^3+7\times10^2+9\)

\(1500=1000+5\times100=10^3+5\times10^2\)

\(1097=1000+9\times10+7=10^3+9\times10^1+7\)

\(20000=2\times10000=2\times10^4\)

\(27000=2\times10000+7\times1000=2\times10^4+7\times10^3\)

\(28700=2\times10000+8\times1000+7\times100\)

\(24004=2\times10000+4\times1000+4=2\times10^4+4\times10^3+4\)

\(26013=2\times10000+6\times1000+1\times10+3=2\times10^4+6\times10^3+10^1+3\)

\(20508=2\times10000+5\times100+8=2\times10^4+5\times10^2+8\)

\(20358=2\times10000+3\times100+5\times10+8=2\times10^4+3\times10^2+5\times10^1+8\)

\(20009=2\times10000+9=2\times10^4+9\)

\(29830=2\times10000+9\times1000+8\times100+3\times10=2\times10^4+9\times10^3+8\times10^2+3\times10^1\)

\(25763=2\times10000+5\times1000+7\times100+6\times10+3=2\times10^4+5\times10^3+7\times10^2+6\times10^1+3\)