![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
`@` `\text {Ans}`
`\downarrow`
\(\dfrac{21^2\cdot14\cdot125}{35^2\cdot125}\)
`=`\(\dfrac{3^2\cdot7^2\cdot2\cdot7\cdot5^2}{5^2\cdot7^2\cdot5^2}\)
`=`\(\dfrac{3^2\cdot2\cdot7\cdot5^2\cdot7^2}{5^2\cdot5^2\cdot7^2}\)
`=`\(\dfrac{3^2\cdot2\cdot7}{5^2}=\dfrac{126}{25}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 1 + 7 + 72+...+7101
=> 7A = 7 + 72+73+...+7102
=> 7A-A= 7102-1
6A = 7102-1
\(\Rightarrow A=\frac{7^{102}-1}{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
210.310-210.39 / 29.310 =210.(310-39) / 29.310
=210.3 / 29.310
=2 / 39
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=1+2^2+2^4+...+2^{2008}\)
\(4C=2^2+2^4+2^6+...+2^{2010}\)
\(4C-C=\left(2^2+2^4+2^6+...+2^{2010}\right)-\left(1+2^2+2^4+...+2^{2008}\right)\)
\(3C=2^{2010}-1\)
\(C=\frac{2^{2010}-1}{3}\)
\(C=1+2^2+2^4+...+2^{2008}\)
\(\Rightarrow4C=2^2+2^4+...+2^{2010}\)
\(\Rightarrow4C-C=\left(2^2+2^4+...+2^{2010}\right)-\left(1+2^2+2^4+...+2^{2008}\right)\)
\(\Rightarrow3C=2^{2010}-1\)
\(\Rightarrow C=\frac{2^{2010}-1}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
(-2)^3.3^3.5^3.7.8/3.5^3.2^4.42
=(-2)^2.(-2).3^3.5^3.7.8/3.5^3.2^2.2^2.7.6
=4.(-2).3^3.5^3.7.8/3.5^3.4.4.7.6
=-1.3^2.8/6
=-72/6=-12
\(\frac{\left(-2\right)^3.3^3.5^3.7.2^3}{3.5^3.2^4.2.3.7}\)=\(\frac{\left(-2\right)^2.\left(-2\right).3^3.5^3.7.2^3}{3^2.5^3.2^5.7}\)=\(\frac{2^5.\left(-2\right).3}{2^5}\)=\(-6\)
Đạt A = 2 + 2 2 + ... + 2 500
2A = 2 2 + 2 3 + .... + 2 501
2A - A = ( 2 2 + 2 3 + .... + 2 501 )
- ( 2 + 2 2 + ... + 2 500 )
A = 2 501 - 2
HAY LẮM