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a. \(5^{10}.125^2.625^3=5^{10}.\left(5^3\right)^2.\left(5^4\right)^3=5^{10}.5^6.5^{12}=5^{10+6+12}=5^{28}\)
a: \(=5^{10}\cdot5^6\cdot5^{12}=5^{28}\)
b: \(=10^3\cdot10^8\cdot10^{15}=10^{26}\)
c: \(=2^{20}\cdot2^{20}=2^{40}\)
d: \(=2^{16}\cdot2^{16}\cdot3^8=2^{32}\cdot3^8\)
e: \(=\dfrac{3^{24}}{3^8}=3^{16}\)
f: \(=2^{12}\cdot2^{20}\cdot2^5=2^{37}\)
Bài 1 :
a/ \(a^3.a^9=a^{3+9}=a^{12}\)
b/\(\left(a^5\right)^7=a^{5.7}=a^{35}\)
c/ \(\left(a^6\right).4.a^{12}=a^{24}.a^{12}.4=a^{24+12}.4=a^{36}.4\)
d/ \(\left(2^3\right)^5.\left(2^3\right)^3=2^{15}.2^9=2^{15+9}=2^{24}\)
e/ \(5^6:5^3+3^3.3^2\)
\(=5^3+3^5=125+243=368\)
i/ \(4.5^2-2.3^2\)
\(=2^2.5^2-2.3^2\)
\(=2^2.25-2^2.14\)
\(=2^2.\left(25-14\right)\)
\(=2^2.11\)
\(=4.11=44\)
Bài 6:
a: \(x=-\dfrac{2}{3}-\dfrac{1}{7}=\dfrac{-14-3}{21}=\dfrac{-17}{21}\)
d: \(x=\dfrac{9}{10}\cdot\dfrac{-5}{9}=\dfrac{-1}{2}\)
e: \(\Leftrightarrow x\cdot\dfrac{1}{3}=\dfrac{14}{21}-\dfrac{3}{21}=\dfrac{11}{21}\)
=>x=11/7
a) a3.a5 = a3+5 = a8
b) x7.x.x4 = x7+1+4 = x12
c) 35.45 = (3.4)5 = 125
d) 85.23 = 25.25.25.23 = 25+5+5+3 = 218
a/a\(^3\).a\(^5\)=a\(^8\)
b/x\(^7\).x.x\(^4\)=x\(^{12}\)
c/3\(^5\).4\(^5\)=2\(^{10}\).3\(^5\)
d/8\(^5\).2\(^3\)=2\(^{18}\)
Bài 4: Viết các tích sau đây dưới dạng 1 lũy thừa của 1 số
A = 82.324 = ( 23 )2 . ( 25 )4 = 26 . 220 = 226
B = 273.94.243 = ( 33 )3 . ( 32 )4 . 35 = 39 . 38 . 35 = 322
C = 410.815 = ( 22 )10 . ( 23 )15 = 220 . 245 = 265
D = 415.530 = ( 22 )15 . 530 = 230 . 530 = ( 2 . 5 )30 = 1030
E = 2716 : 910 = ( 33 )16 . ( 32 )10 = 348 . 320 = 368
F = 25.84 = 25 . ( 23)4 = 25 . 212= 217
g = 256.1253 = ( 52 )6 . ( 53 )3 = 512 . 59 = 521
H = 123.33 = ( 12.3 )3 = 363
a) \(2\left(x-5\right)-3\left(x+7\right)=14\)
\(\Leftrightarrow2x-10-3x-21=14\)
\(\Leftrightarrow-x-31=14\)
\(\Leftrightarrow-x=45\Leftrightarrow x=-45\)
b) \(5\left(x-6\right)-2\left(x+3\right)=12\)
\(\Leftrightarrow5x-30-2x-6=12\)
\(\Leftrightarrow3x-36=12\)
\(\Leftrightarrow3x=48\Leftrightarrow x=16\)
c) \(3\left(x-4\right)-\left(8-x\right)=12\)
\(\Leftrightarrow3x-12-8+x=12\)
\(\Leftrightarrow4x-20=12\)
\(\Leftrightarrow4x=32\Leftrightarrow x=8\)
d) \(-7\left(3x-5\right)+2\left(7x-14\right)=28\)
\(\Leftrightarrow-21x+35+14x-28=28\)
\(\Leftrightarrow-7x+35=0\Leftrightarrow x=5\)
a.\(\hept{\begin{cases}4^8.2^{20}=2^{16}.2^{20}=2^{36}\\9^{12}.27^5.81^4=3^{24}.3^{15}.3^{12}=3^{51}\\64^3.4^5.16^2=2^{18}.2^{10}.2^8=2^{36}\end{cases}}\)
b.\(\hept{\begin{cases}25^{20}.125^4=5^{40}.5^{12}=5^{52}\\x^7x^4x^3=x^{14}\\3^6.4^6=12^6\end{cases}}\)
c.\(\hept{\begin{cases}8^4.2^3.16^2=2^{12}.2^3.2^8=2^{23}\\2^3.2^2.8^3=2^3.2^2.2^9=2^{14}\end{cases}}\)
a) \(a^3.a^5=a^{3+5}=a^8\)
b) \(x^7.x.x^4=x^{7+1+4}=x^{12}\)
c) \(3^5.4^5=\left(3.4\right)^5=12^5=248831\)
d) \(8^5.2^3=8^2.\left(8.2\right)^3=64.16^3=262144\)
a)a3*a5=a8
b)x7*x*x4=x12
c)35*45=(3*4)5=125
d)85*23=215*23=218
Bài 1:
a) b) c) sẽ có bạn giải cho em thôi vì nó dễ tính tay cũng đc
d) \(\frac{4}{2.5}+\frac{4}{5.8}+...+\frac{4}{23.26}\)
\(=\frac{4}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{23.26}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{23}-\frac{1}{26}\right)\)
\(=\frac{4}{3}.\left(\frac{1}{2}-\frac{1}{26}\right)\)
\(=\frac{4}{3}.\frac{6}{13}\)
\(=\frac{8}{13}\)
Bài 2:
a) b) c)
d)\(|\frac{5}{8}x+\frac{6}{7}|-\frac{4}{7}=\frac{10}{7}\)
\(\Leftrightarrow|\frac{5}{8}x+\frac{6}{7}|=2\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{5}{8}x+\frac{6}{7}=2\\\frac{5}{8}x+\frac{6}{7}=-2\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}\frac{5}{8}x=\frac{8}{7}\\\frac{5}{8}x=\frac{-20}{7}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{64}{35}\\x=\frac{-32}{7}\end{cases}}}\)
Vậy \(x\in\left\{\frac{64}{35};\frac{-32}{7}\right\}\)
Bài 1 :
a) \(\left(\frac{2}{5}-\frac{5}{8}\right):\frac{11}{30}+\frac{1}{8}\)
\(=\frac{-9}{40}:\frac{11}{30}+\frac{1}{8}\)
\(=\frac{-27}{44}+\frac{1}{8}\)
\(=\frac{-43}{88}\)
