a) \(2^{2017}+2^{2014}=2^{2014}\left(2^3+1\right)=2^{2014}.9⋮9\)

b) \(4^{2016}+4^{2014}=4^{2014}\left(4^2+1\right)=4^{2014}.17\)

2) \(3.4^{n+2}+4^n=49\\ \Rightarrow4^n\left(3.4^2+1\right)=49\\ \Rightarrow4^n.33=49\\ \Rightarrow4^n=16\\ \Rightarrow n=2\)

3) \(200-180:\left[36.5-7.25\right]\\ =200-180:\left[180-175\right]\\ =200-180:5\\ =200-36\\ =164\)

đó giúp mk đi mà

à, mk quên chưa nói là ai giúp mk sẽ được luôn 2SP đó

giúp mk nha

cảm ơn nhiều!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

những thánh giỏi toán ơi giúp mk được ko

mk năn nỉ đó

Bài 1:

a) Ta có: \(\frac{-5}{7}+\frac{2}{7}+\frac{4}{-9}+\frac{4}{9}\)

\(=-\frac{3}{7}+\frac{-4}{9}+\frac{4}{9}\)

\(=-\frac{3}{7}\)

b) Ta có: \(\left(\frac{1}{2}:\frac{3}{4}\right)^2\)

\(=\left(\frac{1}{2}\cdot\frac{4}{3}\right)^2\)

\(=\left(\frac{2}{3}\right)^2=\frac{4}{9}\)

c) Ta có: \(\frac{1}{2}+\frac{3}{4}-\left(\frac{4}{5}+\frac{3}{4}\right)\)

\(=\frac{1}{2}+\frac{3}{4}-\frac{4}{5}-\frac{3}{4}\)

\(=\frac{1}{2}-\frac{4}{5}\)

\(=\frac{5}{10}-\frac{8}{10}=\frac{-3}{10}\)

d) Ta có: \(5^6:5^4+2^3\cdot2^2-225:15^2\)

\(=5^2+2^5-\frac{15^2}{15^2}\)

\(=25+32-1\)

\(=56\)

e) Ta có: \(\frac{7}{23}+\frac{4}{17}-\frac{7}{23}+\frac{13}{17}\)

\(=\frac{4}{17}+\frac{13}{17}\)

\(=\frac{17}{17}=1\)

g) Ta có: \(19\frac{1}{4}\cdot\frac{7}{12}-15\frac{1}{4}\cdot\frac{7}{12}\)

\(=\frac{7}{12}\left(19+\frac{1}{4}-15-\frac{1}{4}\right)\)

\(=\frac{7}{12}\cdot4=\frac{7}{3}\)

a: \(S=\left(1+3\right)+3^2\left(1+3\right)+3^4\left(1+3\right)+...+3^8\left(1+3\right)\)

\(=4\left(1+3^2+3^4+...+3^8\right)⋮4\)

b: \(S=\left(1+2\right)+2^2\left(1+2\right)+...+2^8\left(1+2\right)\)

\(=3\left(1+2^2+...+2^8\right)⋮3\)

https://hoc247.net/hoi-dap/toan-6/chung-minh-s-1-2-2-2-2-3-2-4-2-5-2-6-2-7-chia-het-cho-3-faq250754.html

S= \(1+2+2^2+...+2^7\)

2S= \(2\cdot\left(2+2^2+...+2^7\right)\)

2S= \(2^1+2^2+...2^8\)

1S= 2S - S = \(\left(2^1+2^2+...2^8\right)-\left(1+2+2^2+...+2^7\right)\)

1S= \(2^1+2^2+...+2^8-1-2-2^2-...-2^7\)

1S= \(2^8-1\)

1S= \(256-1\)

1S= 255

=> 1S chia hết cho 3

Mà 1S= S

=> S chia hết cho 3

Vậy S chia hết cho 3

a. 5² + (x+3) = 5²

=> x + 3    = 5² - 5²

=>  x + 3   =  0

=>  x  = -3

b. 2³ + (x-3²) = 5³ - 4³

=> 8 + (x-9) =  125 - 64

=> x - 9 = 125 - 64 - 8

=> x - 9 =  53

=> x    =  53 + 9

=> x    =   62

Bài 1 tự làm!

Bài 2:

a, \(\left(3x-4\right)\left(x-1\right)^3=0\Rightarrow\left[{}\begin{matrix}3x-4=0\\\left(x-1\right)^3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=1\end{matrix}\right.\)

b, \(2^{2x-1}:4=8^3\Rightarrow2^{2x-1}:2^2=2^9\)

\(\Rightarrow2x-1-2=9\Rightarrow2x-3=9\Rightarrow2x-12\Rightarrow x=6\)

c, Đề chưa rõ

d, \(\left(x+2\right)^5=2^{10}\Rightarrow\left(x+2\right)^5=4^5\Rightarrow x+2=4\Rightarrow x=2\)

e, \(\left(3x-2^4\right).7^3=2.7^4\Rightarrow3x-2^4=2.7^4:7^3\Rightarrow3x-16=2.7=14\)

\(\Rightarrow3x=14+16=30\Rightarrow x=\dfrac{30}{3}=10\)

f, \(\left(x+1\right)^2=\left(x+1\right)^0\Rightarrow\left(x+1\right)^2=1\) (vì x⁰ = 1)

\(\Rightarrow x+1=1\Rightarrow x=0\)

Làm phần c nè!

c, \(\left(x-5\right)^4=\left(x-5\right)^6\Rightarrow\left(x-5\right)^4-\left(x-5\right)^6=0\)

\(\Rightarrow\left(x-5\right)^4.\left(x-5\right)^2=0\)

\(\Rightarrow x-5=0\Rightarrow x=5\)

a, \(3^4\div3^2-\left[120-\left(2^6.2+5^2.2\right)\right]\)

\(=3^2-\left\{120-\text{[}2.\left(2^6+5^2\right)\text{]}\right\}\)

\(=3^2-\left(120-2\cdot89\right)\)

\(=9--58=9+58=67\)

1. \(a,3^4:3^2-\left[120-(2^6\cdot2+5^2\cdot2)\right]\)

\(=3^2-\left[120-\left\{(2^6+5^2)\cdot2\right\}\right]\)

\(=3^2-\left[120-\left\{(64+25)\cdot2\right\}\right]\)

\(=9-\left[120-89\cdot2\right]\)

\(=9-\left[120-178\right]=9-(-58)=67\)

b, Tương tự như bài a

2.a,\(4^x\cdot5+4^2\cdot2=2^3\cdot7+56\)

\(\Leftrightarrow4^x\cdot5+16\cdot2=8\cdot7+56\)

\(\Leftrightarrow4^x\cdot5+32=56+56\)

\(\Leftrightarrow4^x\cdot5+32=112\)

\(\Leftrightarrow4^x\cdot5=80\)

\(\Leftrightarrow4^x=16\Leftrightarrow4^x=4^2\Leftrightarrow x=2\)

\(b,24:(2x-1)^3-2=1\)

\(\Leftrightarrow24:(2x-1)^3=3\)

\(\Leftrightarrow(2x-1)^3=8\)

\(\Leftrightarrow(2x-1)^3=2^3\)

\(\Leftrightarrow2x-1=2\)

Làm nốt là xong thôi