4².8³ = (2²)².(2³)³ = 2⁴.2⁹ = 2¹³

9³.27² = (3²)³.(3³)² = 3⁶.3⁶ = 3¹²

8².25³ = (2³)².(5²)³ = 2⁶.5⁶ = (2.5)⁶ = 10⁶

a ) 4² . 8³ = ( 2² ) ² . ( 2³ ) ³ = 2^2.2 . 2^3.3 = 2⁴ . 2⁹ = 2⁴⁺⁹ = 2¹³

b ) 9³ . 27² = ( 3² ) ³ . ( 3³ ) ² = 3^2.3 . 3^3.2 = 3⁶ . 3⁶ = 3⁶⁺⁶ = 3¹²

4² . 8³ = ( 2² ) ² . ( 2³ ) ³

      = 2⁴ . 2⁹

       = 2¹³

9³ . 27² = ( 3² ) ³ . ( 3³ ) ²

            = 3⁶ . 3⁶

              = 3¹²

8^{2 .} 25³ = ( 2³ ) ² . ( 5² ) ³

           = 2⁶ . 5⁶

          = ( 2 . 5 ) ⁶

          = 10⁶

\(a)9.4.25.8.125\)

\(=9.\left(4.25\right).\left(8.125\right)\)

\(=9.100.1000\)

\(=900.1000\)

\(=900000\)

\(a,9.4.25.8.125=9.\left(4.25\right).\left(8.125\right)=9.100.1000=900000\)

\(b,25.5.27.2\)(câu này hình như thiếu đề, ko tính nhanh đc)

\(c,37.7+80.3+43.7\)\(=7.\left(37+43\right)+80.3\)\(=7.80+3.80=80\left(7+3\right)=80.10=800\)

\(d,113.38+113.62+87.62+87.38\)\(=113\left(38+62\right)+87\left(62+38\right)\)

\(=113.100+87.100=100.\left(113+87\right)=100.200=20000\)

Viết gọn lũy thừa:

\(a,x.x.y.y.x.y.x=\left(x.x.x.x\right).\left(y.y.y\right)=x^4.y^4\)

\(b,7^5:343=7^5:7^3=7^{5-3}=7^2\)

\(c,A^{12}:A^{18}=A^{12-18}=A^{-6}\)

\(d,x^7.x^4.x=x^{7+4+1}=x^{12}\)

a, x= 3

b, ko có x thỏa mãn

c, x= 3

d, x= 2

a: x=3

b: \(2x-1=2\)

hay \(x=\dfrac{3}{2}\)

c: \(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)

2018¹⁰⁰⁹ và (2.2017)¹⁰⁰⁹

Vì 2018 < 2.2017 => 2018¹⁰⁰⁹ < (2.2017)¹⁰⁰⁹

c ko bt cách gõ mũ trên olm à????

chiu that day

 mn giải bài hộ mình với ạ

3B=3^4+3^5+...+3^101

=>2B=3^101-3^3

=>2B+27=3^101 là lũy thừa của 3

giúp mình với mình sắp thi giữa kì rồi

a) Ta có :

\(27^{27}>27^{26}=\left(27^2\right)^{13}=729^{13}>243^{13}\)

\(\Rightarrow27^{27}>243^{13}\)

\(\Rightarrow-27^{27}< -243^{13}\)

\(\Rightarrow\left(-27\right)^{27}< \left(-243\right)^{13}\)

b) \(\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{8}\right)^{26}=\left(\dfrac{1}{8^2}\right)^{13}=\left(\dfrac{1}{64}\right)^{13}>\left(\dfrac{1}{128}\right)^{13}\)

\(\Rightarrow\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{128}\right)^{13}\)

\(\Rightarrow\left(-\dfrac{1}{8}\right)^{25}< \left(-\dfrac{1}{128}\right)^{13}\)

c) \(4^{50}=\left(4^5\right)^{10}=1024^{10}\)

\(8^{30}=\left(8^3\right)^{10}=512^{10}< 1024^{10}\)

\(\Rightarrow4^{50}>8^{30}\)

d) \(\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{9}\right)^{12}< \left(\dfrac{1}{27}\right)^{12}\)

\(\Rightarrow\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{27}\right)^{12}\)

a) Ta có :

2727>2726=(272)13=72913>243132727>2726=(272)13=72913>24313

⇒2727>24313⇒2727>24313

⇒−2727<−24313⇒−2727<−24313

⇒(−27)27<(−243)13⇒(−27)27<(−243)13

b) (18)25>(18)26=(182)13=(164)13>(1128)13(81​)25>(81​)26=(821​)13=(641​)13>(1281​)13

⇒(18)25>(1128)13⇒(81​)25>(1281​)13

⇒(−18)25<(−1128)13⇒(−81​)25<(−1281​)13

c) 450=(45)10=102410450=(45)10=102410

830=(83)10=51210<102410830=(83)10=51210<102410

⇒450>830⇒450>830

d) (19)17<(19)12<(127)12(91​)17<(91​)12<(271​)12

⇒(19)17<(127)12⇒(91​)17<(271​)12

Bài 1:

a) 8² . 2² = 64 . 4 = 256

b) 2⁵. 4 = 2⁵. 2²= 2⁵⁺² = 2⁷

c) 9⁴. 243 = 9⁴. 3⁵=(3²)⁴.3⁵=3⁸.3⁵=3⁸⁺⁵=3¹³

Bài 1 :

\(a.8^2.2^2=\left(8.2\right)^2=16^2\)

\(b.2^5.4=2^5.2^2=2^7\)

\(c.9^4.243=\left(3^2\right)^4.3^5=3^8.3^5=3^{13}\)

Bài 2:

a. ( đề sai =.= )

\(b.12.\left(x-1\right):3=43+2^3\)

\(\Leftrightarrow12.\left(x-1\right)=43+2^3.3\)

\(\Leftrightarrow12.\left(x-1\right)=67\)

\(\Leftrightarrow x-1=\frac{67}{12}\)

\(\Leftrightarrow x=\frac{79}{12}\)