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\(18^{20}.45^5.5^{25}.8^{10}\)
\(=3^{40}.2^{20}.5^5.3^{10}.5^{25}.2^{30}\)
\(=3^{50}.2^{50}.5^{30}\)
\(=6^{50}.5^{30}\)
\(=\left(6^5\right)^{10}.\left(5^3\right)^{10}\)
\(=\left(6^5.5^3\right)^{10}\)
\(\left(x^2y\right)^5.\left(x^2.y^2\right)^7.\left(x.y\right)^6.x^3\)
\(=x^{10}.y^5.x^{14}.y^{14}.x^6.y^3.x^3\)
\(=x^{33}.y^{22}\)
\(=\left(x^3\right)^{11}.\left(y^2\right)^{11}\)
\(=\left(x^3.y^2\right)^{11}\)
\(2^7.3^8.4^9.9^8\)
\(=2^7.3^8.2^{18}.3^{16}\)
\(=2^{25}.3^{24}\)( mk chỉ làm được đến thế thôi )
Tham khảo nhé~
a) \(18^{20}.45^5.5^{25}.8^{10}\)
\(=\left(2.3^2\right)^{20}.\left(3^2.5\right)^5.5^{25}.\left(2^3\right)^{10}\)
\(=2^{20}.3^{40}.3^{10}.5^5.5^{25}.2^{30}\)
\(=2^{50}.3^{50}.5^{30}\)
\(=6^{50}.5^{30}\)
\(=\left(6^5\right)^{10}.\left(5^3\right)^{10}\)
\(=7776^{10}.125^{10}\)
\(=972000^{10}\)
b ) \(\left(x^2y\right)^5.\left(x^2.y^2\right)^7.\left(xy\right)^6.x^3\)
\(=x^{10}.y^5.x^{14}.y^{14}.x^6.y^6.x^3\)
\(=x^{33}.y^{25}\)
\(=x^{25}.y^{25}.x^8\)
\(=...\)
c) \(2^7.3^8.4^9.9^8\)
\(=2^7.3^8.\left(2^2\right)^9.\left(3^2\right)^8\)
\(=2^7.3^8.2^{18}.3^{16}\)
\(=2^{25}.3^{24}\)
\(=...\)( Câu c này hình như đề bài sai sót . Không chuyển thành lũy thừa được )
a,ta có:
\(3^5.5^7.5.3^2\)
\(=\left(3^5.3^2\right).\left(5.5^7\right)\)
\(=3^7.5^8\)
\(b=2^8.\left(2.2\right)^5.9^9\)
\(=2^8.2^{10}.9^9\)
\(=2^{18}.9^9\)
a) \(\frac{5}{6}-\left|1-x\right|=\frac{1}{2}\)
<=> \(\left|1-x\right|=\frac{5}{6}-\frac{1}{2}\)
<=>\(\left|1-x\right|=\frac{1}{3}\)
<=>\(\orbr{\begin{cases}1-x=\frac{1}{3}\\1-x=-\frac{1}{3}\end{cases}}\)
<=>\(\orbr{\begin{cases}x=1-\frac{1}{3}\\x=1-\left(-\frac{1}{3}\right)\end{cases}}\)
<=>\(\orbr{\begin{cases}x=\frac{2}{3}\\x=\frac{4}{3}\end{cases}}\)
Vậy \(x=\frac{2}{3}\)hoặc\(x=\frac{4}{3}\)
b) \(\frac{8^5.\left(-5\right)^8+\left(-2\right)^5.\left(-10\right)^9}{4^{10}.5^7+20^8.4}.\frac{144}{25}\)
\(=\frac{2^{15}.5^8+2^5.2^9.5^9}{2^{20}.5^7+2^{16}.5^8.2^2}.\frac{2^4.3^2}{5^2}\)
\(=\frac{2^{14}.5^8.\left(2+5\right)}{2^{18}.5^7.\left(2^2+5\right)}.\frac{2^4.3^2}{5^2}\)
\(=\frac{2^{14}.5^8.7}{2^{18}.5^7.3^2}.\frac{2^4.3^2}{5^2}\)
\(=\frac{2^{18}.3^2.5^8.7}{2^{18}.3^2.5^9}\)
\(=\frac{7}{5}\)
Học tốt!!!!
a.\(\frac{5}{6}-\left|1-x\right|=\frac{1}{2}\)
\(=>\left|1-x\right|=\frac{5}{6}-\frac{1}{2}\)
\(=>\left|1-x\right|=\frac{1}{3}\)
\(=>\orbr{\begin{cases}1-x=\frac{1}{3}\\1-x=\frac{-1}{3}\end{cases}}\)
\(=>\orbr{\begin{cases}x=1-\frac{1}{3}=\frac{2}{3}\\x=1-\frac{-1}{3}=\frac{4}{3}\end{cases}}\)
ban nao co chuyen shin ko cho minh muon minh giai cho 10 bai nhu the i love pac pac
\(A=\frac{2^{12}.3^4-4^5.9^2}{\left(2^2.3\right)^6+8^4.3^5}\)
\(A=\frac{2^{12}.3^4-2^{10}.3^4}{2^{12}.3^6+2^{12}.3^5}\)
\(A=\frac{2^{10}.3^4\left(2^2-1\right)}{2^{10}.3^4\left(2^2.3^2+2^2.3\right)}\)
\(A=\frac{2^2-1}{2^2.3^2+2^2.3}\)
\(A=\frac{4-1}{36+12}\)
\(A=\frac{3}{48}=\frac{1}{16}\)
\(\left(\dfrac{2}{3}\right)^3.\left(\dfrac{-3}{4}\right)^2.\left(-1\right)^{2013}=\dfrac{8}{27}.\dfrac{9}{16}.\left(-1\right)=-\dfrac{1}{6}\)
\(\left(\dfrac{1}{5}\right)^{15}.\left(\dfrac{1}{4}\right)^{20}=\dfrac{1}{5^{12}}.\dfrac{1}{4^{20}}=5^{-12}.4^{-20}=125^{-4}.1024^{-4}=\left(125.1024\right)^{-4}=128000^{-4}\)
\(\dfrac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}=\dfrac{2^{12}.3^{10}+2^3.3.5.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}+2^{12}.2^{10}.5}{2^{12}.3^{12}+2^{11}.3^{11}}=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3+1\right)}=\dfrac{2.6}{3.7}=\dfrac{4}{7}\)
a) 2x - 15 = 17
2x = 25
b) ( 7x - 11 )3 = 25. 52 + 200
(7x - 11)3 = 32 . 25 + 200
(7x -11)3 = 1000
(7x-11)3 = 103
7x - 11 = 10
7x = 10+11
7x = 21
x = 21 : 7
x = 3
like nha
( Mik làm mấy phần mà bạn dưới chưa làm)
11) xy+x+y=9
\(\Leftrightarrow\) xy+x+y+1=9+1
\(\Leftrightarrow\left(xy+x\right)+\left(y+1\right)\)=10
\(\Leftrightarrow x\left(y+1\right)+\left(y+1\right)=10\)
\(\Leftrightarrow\) (x+1)(y+1)=10=1.10=10.1=-1.-10=-10.-1=2.5=5.2=-2.-5=-5.-2
\(\Rightarrow\) TH1: x+1=1 ; y+1=10
\(\Leftrightarrow x=0;y=9\)
TH2: x+1=10;y+1=1
\(\Leftrightarrow\)x=9;y=0
TH3: x+1=-1;y+1=-10
\(\Leftrightarrow\) x=-2;y=-11
...........
Vậy:........
( Bạn tự làm nốt chứ dài quá, mik chỉ hướng dẫn cách làm bài thôi)
1) -x = -7
=> x = 7
2) - x = 17
=> x = - 17
3) |x| = 17
=> x = ±17
4) -(-x) = |-17|
=> x = 17
5) - 19 - x = 17
=> - x = 17 + 19
=> x = - 36
6) - 19 - x = - 17
=> - x = - 17 + 19
=> -x = 2
=> x = - 2
7) - 5 - (10 - x) = 7
=> - 5 - 10 + x = 7
=> - 15 + x = 7
=> x = 7 + 15
=> x = 22
8) |x + 3| + 7 = 12
=> |x + 3| = 12 - 7
=> |x + 3| = 5
=> x + 3 = 5 hoặc x + 3 =- 5
=> x = 2 hoặc x = - 8
9) 2 - |x - 2| = x
=> - |x - 2| - x = - 2
TH1: x >= 2
- (x - 2) - x = - 2
=> - x + 2 - x =- 2
=> - 2x = - 4
=> x = 2 (nhận)
TH2: x < 2
-[-(x - 2)] - x = - 2
=> x - 2 - x = - 2
=> 0x = 0 (vô số nghiệm)
1/ \(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\frac{5^{20}.3^{29}-3^{31}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{19}}=\frac{3^{29}.5^{18}.\left(25-9\right)}{3^{29}.5^{18}.\left(7-5\right)}=\frac{16}{2}=8\)
CÁC BÀI CÒN LẠI TƯƠNG TỰ HẾT NHÉ E
a)\(3^5.5^7.45=3^5.5^7.3^2.5=3^7.5^8\)
b)\(2^8.4^5.9^9\)\(=2^8.2^{10}.9^9=2^{18}.9^9\)
c)\(\left(2^3.3^5.5^7\right)^{10}.12^{20}=2^{13}.3^{15}.5^{17}.12^{20}\)\(=2^{13}.3^{15}.5^{17}.2^{40}.3^{20}=2^{53}.3^{35}.5^{17}\)
d)\(\left(x^2y\right)^5.\left(x^2y^2\right)^7.\left(x.y^2\right)^6.x^3=x^{10}.y^5.x^{14}.y^{14}.x^6.y^{12}.x^3\)
\(=x^{33}.y^{31}\)
e)\(18^{20}.45^5.5^{25}.8^{10}=2^{20}.3^{40}.5^5.3^{10}.5^5.5^{25}.2^{30}\)
\(=2^{50}.3^{50}.5^{35}=6^{50}.5^{35}\)
f)\(2^7.3^8.4^9.9^8=2^7.3^8.2^{18}.3^{16}=2^{25}.3^{24}\)