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Lời giải:
\(2^{27}.3^{18}=(2^3)^9.(3^2)^9=8^9.9^9=(8.9)^9=72^9\)
\(25^4.2^8=25^4.(2^2)^4=25^4.4^4=(25.4)^4=100^4\)
\((-9)^4.27^2=9^4.27^2=(3^2)^4.(3^3)^2=3^8.3^6=3^{8+6}=3^{14}\)
\(-5^4:25=-5^4:(5^2)=-5^{4-2}=-5^2\)
\(\frac{2^{15}.5^8+2^{14}.5^9}{2^{16}.5^7+2^{16}.5^8}=\frac{2^{14}.5^8\left(2+5\right)}{2^{16}.5^7\left(1+5\right)}=\frac{2^{14}.5^8.7}{2^{16}.5^7.6}=\frac{5.7}{4.6}=\frac{35}{24}\)
Rút gọn :
\(\frac{-63}{81}=\frac{-7\cdot9}{9\cdot9}=\frac{-7}{9}\)
\(\frac{-5\cdot6}{9\cdot35}=\frac{-5\cdot2\cdot3}{3\cdot3\cdot5\cdot7}=\frac{-2}{3\cdot7}=\frac{-2}{21}\)
\(\frac{7\cdot2+8}{2\cdot14\cdot5}=\frac{14+8}{2\cdot2\cdot7\cdot5}=\frac{22}{2\cdot2\cdot7\cdot5}=\frac{2\cdot11}{2\cdot2\cdot7\cdot5}=\frac{11}{2\cdot7\cdot5}=\frac{11}{70}\)
\(\frac{-63}{81}=\frac{-7}{9}\)
\(\frac{-5.6}{9.35}=\frac{-5.2.3}{3.3..5.7}=\frac{-2}{3.7}=\frac{-2}{21}\)
\(\frac{7.2+8}{2.14.5}=\frac{22}{2.2.7.5}=\frac{2.11}{2.2.7.5}=\frac{11}{70}\)
1) 25 x 27 = 25+7 = 212
2 x 23 x 25 = 21 x 23 x 25 = 21+3+5 = 29
2) a) 8 = 23
b) 121 = 112
c) 243 = 35
d) 36 = 22 x 32
Học tốt!!!
1,
\(A=2^0+2^1+2^2+..+2^{2006}\)
\(=1+2+2^2+...+2^{2016}\)
\(2A=2+2^2+2^3+..+2^{2007}\)
\(2A-A=\left(2+2^2+2^3+..+2^{2007}\right)-\left(1+2+2^2+..+2^{2006}\right)\)
\(A=2^{2017}-1\)
\(B=1+3+3^2+..+3^{100}\)
\(3B=3+3^2+3^3+..+3^{101}\)
\(3B-B=\left(3+3^2+..+3^{101}\right)-\left(1+3+..+3^{100}\right)\)
\(2B=3^{101}-1\)
\(\Rightarrow B=\frac{3^{100}-1}{2}\)
\(D=1+5+5^2+...+5^{2000}\)
\(5D=5+5^2+5^3+...+5^{2001}\)
\(5D-D=\left(5+5^2+..+5^{2001}\right)-\left(1+5+...+5^{2000}\right)\)
\(4D=5^{2001}-1\)
\(D=\frac{5^{2001}-1}{4}\)
25.8=25.23=25+3=28
37/9=37:32=37–2=35
25x8=25x23=28
37:9=37:33=34