b. 2³ . 17 - 2³ . 14

= 8 . 17 - 8 . 14

= 8 . (17 - 14)

= 8 . 3

= 24

d. 17.55 + 43.17 + 12 . 17

= 17 . (55 + 43 + 12)

= 17 . 110

= 1870

e. 248 + (-12) + 2064 + (-236)

= 248 - 12 + 2064 - 236

= 236 + 2064 - 236

= 236 - 236 + 2064

= 0 + 2064

= 2064

a. 275 + (195 - 4x) = 350

               195 - 4x = 350 - 275

                195 - 4x = 75

                         4x = 195 - 75

                         4x = 120

                           x = 30

21.{350 : [274 - 2³(35 - 28 : 4)]}
= 21.{350 : [274 - 8(35 - 7)]}
= 21.{350 : [274 - 8.28]}
= 21.{350 : [274 - 224]}
= 21.{350 : 50}
= 21.7
= 147

21.{350:[274-2³.(35-28:4)

=21.{350:[274-8.28]

=21.{350:[274-224]

=21.{350:50}

=21.7=147

125⁶ và 25⁸

125⁶=125.125.125.125.125.125=5³.5³.5³.5³.5³.5³=5^3+3+3+3+3+3=5¹⁸

25⁸=25.25...25(8 chữ số 25)=5².5²...5²(8 chữ số 5²)=5^{2+2+2+2+2+2+2+2}=5¹⁶

Vì 5¹⁸>5¹⁶

=> 125⁶>25⁸

350² và 2⁷⁵

350²=350.350=2.5².7.2.5².7=2².5⁴.7²

2⁷⁵=2.2.2....2(75 chữ số 2)=2⁴.2¹⁰.2⁶..2⁵⁰

Vì 2².5⁴.7²<2⁴.2¹⁰.2⁶(2²<2⁴;5⁴<2¹⁰;7²<2⁶)

=>350²<2⁷⁵

Chúc bạn học tốt!

Bài 1: 

a) Ta có: \(\left(2x-1\right)^{20}=\left(2x-1\right)^{18}\)

\(\Leftrightarrow\left(2x-1\right)^{20}-\left(2x-1\right)^{18}=0\)

\(\Leftrightarrow\left(2x-1\right)^{18}\left[\left(2x-1\right)^2-1\right]=0\)

\(\Leftrightarrow\left(2x-1\right)^{18}\cdot\left(2x-2\right)\cdot2x=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\x=1\end{matrix}\right.\)

b) Ta có: \(\left(2x-3\right)^2=9\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)

c) Ta có: \(\left(x-5\right)^2=\left(1-3x\right)^2\)

\(\Leftrightarrow\left(x-5\right)^2-\left(3x-1\right)^2=0\)

\(\Leftrightarrow\left(x-5-3x+1\right)\left(x-5+3x-1\right)=0\)

\(\Leftrightarrow\left(-2x-4\right)\left(4x-6\right)=0\)

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

Bài 2: 

a) \(15^{20}-15^{19}=15^{19}\left(15-1\right)=15^{19}\cdot14⋮14\)

b) \(3^{20}+3^{21}+3^{22}=3^{20}\left(1+3+3^2\right)=3^{20}\cdot13⋮13\)

c) \(3+3^2+3^3+...+3^{2007}\)

\(=3\left(1+3+3^2\right)+...+3^{2005}\left(1+3+3^2\right)\)

\(=13\left(3+...+3^{2005}\right)⋮13\)

\(\frac{4^{20}}{6^{20}}-\frac{2^{20}}{3^{20}}+\frac{6^{20}}{9^{20}}=\left(\frac{2}{3}\right)^{20}-\left(\frac{2}{3}\right)^{20}+\left(\frac{2}{3}\right)^{20}=\left(\frac{2}{3}\right)^{20}\)

\(A=2+2^2+2^3+...+2^{20}\)

\(=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{19}+2^{20}\right)\)

\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{19}\left(1+2\right)\)

\(=3\left(2+2^3+...+2^{19}\right)⋮3\)

\(A=2+2^2+2^3+...+2^{20}\)

\(=\left(2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8\right)+...+\left(2^{17}+2^{18}+2^{19}+2^{20}\right)\)

\(=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+...+2^{17}\left(1+2+2^2+2^3\right)\)

\(=15\left(2+2^5+...+2^{17}\right)⋮5\)

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