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20:
1: Xét ΔACD và ΔABE có
AC=AB
góc A chung
AD=AE
=>ΔACD=ΔABE
2: ΔABE=ΔACD
=>góc ABE=góc ACD
=>góc IBD=góc ICE
3: Xét ΔIBD và ΔICE có
góc IBD=góc ICE
BD=CE
góc IDB=góc IEC
=>ΔIBD=ΔICE
4: ΔIBD=ΔICE
=>IB=IC; ID=IE
=>ΔIBC cân tại I; ΔIDE cân tại I
\(\left(\dfrac{1}{3}\right)^{50}.\left(-9\right)^{25}-\dfrac{2}{3}:4\)
\(=\left(\dfrac{1}{3}\right)^{50}.\left[\left(-3\right)^2\right]^{25}-\dfrac{2}{3}.\dfrac{1}{4}\)
\(=\left(\dfrac{1}{3}\right)^{50}.\left(-3\right)^{50}-\dfrac{2}{12}\)
\(=\left[\dfrac{1}{3}.\left(-3\right)\right]^{50}-\dfrac{1}{6}\)
\(=\left(-1\right)^{50}-\dfrac{1}{6}\)
\(=1-\dfrac{1}{6}\)
\(=\dfrac{6}{6}-\dfrac{1}{6}\)
\(=\dfrac{5}{6}\)
\(\left(\dfrac{1}{3}\right)^{50}\cdot\left(-9\right)^{25}-\dfrac{2}{3}:4=\)
=\(\dfrac{1}{3^{50}}\cdot\left(-9\right)^{25}-\dfrac{2}{3}\cdot\dfrac{1}{4}\)
=\(\dfrac{\left(-9\right)^{25}}{9^{25}}-\dfrac{1}{6}\)
=\(-1-\dfrac{1}{6}\)
=\(-\dfrac{6}{6}-\dfrac{1}{6}\)
=\(-\dfrac{7}{6}\)
\(a,10^8.2^8=\left(10.2\right)^8=20^8\)
\(b,10^8:2^8=\left(10:2\right)^8=5^8\)
\(c,25^4.2^8=25^4.\left(2^2\right)^4=25^4.4^4=\left(25.4\right)^4=100^4\)
\(d,15^8.9^4=15^8.\left(3^2\right)^4=15^8.3^8=\left(15.3\right)^8=45^8\)
\(e,27^2.25^3=\left(3^3\right)^2.\left(5^2\right)^3=3^6.5^6=\left(3.5\right)^6=15^6\)
a, 108 . 28
= ( 10 . 2 ) 8
= 208
b, 108 : 28
= ( 10 : 2 )8
= 58
c, 254 . 28
= ( 52 )4 . 28
= 58 . 28
= ( 5 . 2 ) 8
= 108
d, 158 . 94
= 158 . ( 32 )4
= 158 . 38
= ( 15 . 3 ) 8
= 458
e, 272 . 253
= ( 33 )2 . ( 52 ) 3
= 36 . 56
= ( 3 . 5 ) 6
= 15 6
\(\left(x-1\right)^2=5^2\\\Rightarrow x-1=5\\ \Rightarrow x=5+1=6\)