\(3^2.2^4-2^3.4^2-2^3.5^0+4^2.2^2\)

\(=9.16-8.16-8.1+16.4\)

\(=16.\left(9-8\right)-8+64\)

\(=16.1-8+64\)

\(=8+64\)

\(=72\)

ĐA TẠ SƯ PHỤ VÕ NGỌC PHƯƠNG

5^2x-3=50+75

5^2x=125

=>x=125:25

=>x=5

\(\left(5^2x-3\right)-3.5^2=5^2.2\)

<=>\(\left(25x-3\right)-3.25=25.2\)

<=>\(\left(25x-3\right)-75=50\)

<=>\(\left(25x-3\right)=125\)

<=>\(25x-3=125\)

<=>\(x-3=125:25\)

<=>\(x-3=5\)

<=>\(x=8\)

\(\Leftrightarrow x=8\)

Hk tốt

`#3107.101107`

\(\dfrac{27^2\cdot2^3\cdot5^4}{15^2\cdot6^9}\)

\(=\dfrac{\left(3^3\right)^2\cdot2^3\cdot5^4}{3^2\cdot5^2\cdot2^9\cdot3^9}\)

\(=\dfrac{3^6\cdot2^3\cdot5^4}{3^{11}\cdot5^2\cdot2^9}\)

\(=\dfrac{5^2}{3^5\cdot2^6}\)

\(=\dfrac{25}{15552}\)

\(R=\frac{2.2}{1.3}+\frac{3.3}{2.4}+\frac{4.4}{3.5}+...+\frac{2006.2006}{2005.2007}\)

\(R=\frac{2^2}{1.3}+\frac{3^2}{2.4}+\frac{4^2}{3.5}+...+\frac{2006^2}{2005.2007}\)

\(R=\frac{1.3+1}{1.3}+\frac{2.4+1}{2.4}+\frac{3.5+1}{3.5}+...+\frac{2005.2007+1}{2005.2007}\)

\(R=1+\frac{1}{1.3}+1+\frac{1}{2.4}+1+\frac{1}{3.5}+...+1+\frac{1}{2005.2007}\)  

\(R=\left(1+1+...+1\right)+\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{2005.2007}\right)+\left(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{2004.2006}\right)\)

( có 2005 số 1)

\(R=2005+\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2005}-\frac{1}{2007}\right)\)

\(+\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2004}-\frac{1}{2006}\right)\)

\(R=2005+\frac{1}{2}.\left(1-\frac{1}{2007}\right)+\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2006}\right)\)

\(R=2005+\frac{1}{2}\cdot\frac{2006}{2007}+\frac{1}{2}\cdot\frac{501}{1003}\)

\(R=2005+\frac{1003}{2007}+\frac{501}{2006}\)

...

đến đây bn tự tính típ nha!

\(6^2.2^2.5:\left[3.12-\left(2x-6\right)\right]=2^3.5\)

\(\Rightarrow36.4.5:\left[36-\left(2x-6\right)\right]=8.5\)

\(\Rightarrow720:\left[36-\left(2x-6\right)\right]=40\)

\(\Rightarrow36-\left(2x-6\right)=720:40=18\)

\(\Rightarrow2x-6=36-18=18\)

\(\Rightarrow2x=18+6=24\)

\(\Rightarrow x=24:2=12\)

A=2(1+3+5+...+97+99)

Số số lẻ trong khoảng từ 1 đến 99 là (99-1):2+1=50(số)

=>Tổng của các số lẻ từ 1 đến 99 là (99+1)*50/2=50*50=2500

=>A=2*2500=5000

B=2(2+4+6+...+98+100)

Số số chẵn trong khoảng từ 2 đến 100 là

(100-2):2+1=50(số)

=>Tổng của các số lẻ từ 2 đến 100 là (100+2)*50/2=50*51=2550

=>B=2*2550=5100

=>A<B

\(\frac{4^2.2^5+32.125}{2^3.5^2}\) \(=\)\(\frac{4^2.2^5+2^5.5^3}{2^3.5^2}\)

                                     \(=\frac{\left(4^2+5^3\right).2^5}{2^3.5^2}\)

                                     \(=\)  \(\frac{\left(4^2+5^3\right).2^2}{5^2}\)

                                    \(=\)    \(\frac{564}{25}\)

\(\frac{4^2.2^5+32.125}{2^3.5^2}=\frac{4^2.2^5+2^5.5^3}{2^3.2^5}\)

                                   \(=\frac{(4^2+5^3).2^5}{2^3.2^5}\)

                                     \(=\frac{(4^2+5^3).2^2}{5^2}\)

                                       \(=\frac{564}{25}\)

\(B=136.25+75.136-6^2.10^2\)

\(=136.\left(75+25\right)-36.100\)

\(=136.100-36.100\)

\(=\left(136-36\right).100\)

\(=100.100=10000\)

\(C=2^3.5^3-\left\{7^2.2^3.5^2.\left[4^3:8+11^2:121-2\left(37-5.7\right)\right]\right\}\)

\(=10^3-\left\{49.8.25.\left[8+1+2.2\right]\right\}\)

\(=1000-\left(49.200.13\right)\)

\(=1000-127400\)

\(=-126400\)

Bài này đơn giản thôi bạn

B= 136.(25+75)-36.100

B= 136. 100-36.100

B= 100.(136-36)

B= 100.100

B= 10000