viết KQ dưới dạng lũ thừa :
7.7.7.7.49
8.8.2.2.2
9.9.27.3.3.3
5.125.25.5.5.5
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\(9^{20}:\left(0,375\right)^{40}\)
\(=\left(3^2\right)^{20}:\left(\frac{3}{8}\right)^{40}\)
\(=3^{40}:\left(\frac{3}{8}\right)^{40}\)
\(=\left(3:\frac{3}{8}\right)^{40}\)
\(=8^{40}\)
\(=\left(2^3\right)^{40}\)
\(=2^{120}\)
GIẢI RA THÌ HƠI DÀI NHG KO SEO, MK WILL CỐ GẮNG ^_^
= ( 163 . 25 : 240 ) . ( 94 . 275 . 81 . 312 . 924 : 2718 ) . ( 1255 . 252 ) ( Chỗ nài nhiều số quá ko bt mk có bỏ sót ko )
= ( 212 . 25 : 240 ) . ( 38 . 315 . 34 . 312 . 348 : 354 ) . ( 515 . 54 )
= 212 + 5 - 40 . 38 + 15 + 4 + 12 + 48 - 54 . 515 + 4
= 2-23 . 333 . 519
Đó, chắc sai r bn đừng chép vào, nhiều số đâm ra mk hay bj lú
a) (4 * 5)^13 = 20^13 b) (27^16) / (9^10) = 3^(3*16) / 3^(2*10) = 3^48 / 3^20 c) (16^3) / (8^4) = 2^(4*3) / 2^(3*4) = 2^12 / 2^12 = 1
d: =5^10*5^4/5^12=5^2
e: \(=\dfrac{2^{19}\cdot3^9+3^9\cdot2^{18}\cdot5}{2^{19}\cdot3^9+3^{10}\cdot2^{20}}\)
\(=\dfrac{2^{18}\cdot3^9\left(2+5\right)}{2^{19}\cdot3^9\left(1+3\cdot2\right)}=\dfrac{1}{2}\)
`@` `\text {Ans}`
`\downarrow`
`d)`
\(\dfrac{5^{10}\cdot25^2}{125^4}\)
`=`\(\dfrac{5^{10}\cdot\left(5^2\right)^2}{\left(5^3\right)^4}=\dfrac{5^{10}\cdot5^4}{5^{12}}=\dfrac{5^{14}}{5^{12}}=5^2\)
`e)`
\(\dfrac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
`=`\(\dfrac{2^{19}\cdot3^9+3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+2^{20}\cdot3^{10}}\)
`=`\(\dfrac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3^9}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}\)
`=`\(\dfrac{2^{18}\cdot3^9\left(2+5\right)}{2^{19}\cdot3^9\left(1+2\cdot3\right)}\)
`=`\(\dfrac{2^{18}\cdot3^9}{2^{19}\cdot3^9}=\dfrac{1}{2}\)
A = 22+(22+23+24+...+22015+22016)
2A = 23+(23+24+25+...+22016+22017)
2A - A = A = 23[+(23+24+25+...+22016+22017)] - [22+(22+23+24+...+22015+22016)]
A = 23+23+24+25+...+22016+22017-22-22-23-24-...-22015-22016 = 22017-22-22+23 (DÙNG PHƯƠNG PHÁP LƯỢC BỎ)
A = 22017-(22+22-23)
A = 22017-(4+4-8)
A = 22017-0 = 22017
hihihi...
ta có : \(3^2.\frac{1}{243}.81^2.\frac{1}{3^2}=\frac{3^2.\left(3^4\right)^2}{3^5.3^2}=\frac{3^2.3^8}{3^5.3^1}=3^3\)
\(2013=2.1000+10+3=2.10^3+1.10^1+3.10^0\)
\(20112013=2.10000000+100000+10000+2.1000+10+3\)
\(=2.10^7+10^5+10^4+2.10^3+10^1+3.10^0\)
2013 = 2 x 1000 + 10 + 3 = 2 x 10^3 + 1 . 10^1 + 3 . 10^0
20112013 = 2 x 10000000 + 100000 + 2 x 1000 + 10 + 3 = 2 x 10^7 + 10^5 + 10^4 + 2 x 10^3 + 10^1 + 3 x 10^0
ok nhé với lại 10^2 là 10 mũ 2 nhé =>
7.7.7.7.49 = 7.7.7.7.7.7 = 76
8.8.2.2.2 = 8.8.8 = 83 = (23)3 = 29
9.9.27.3.3.3 = 3.3.3.3.3.3.3.3.3.3 = 310
5.125.25.5.5.5 = 5.5.5.5.5.5.5.5.5 = 59
\(7.7.7.7.49=7^6\)
\(8.8.2.2.2=8^3=2^9\)
\(9.9.27.3.3.3=3^{10}=9^5\)
\(5.125.25.5.5.5=5^9\)