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a, 108.28 =(10.2)8 = 208
b, 254.28 = (52)4,28 = 58.28 = 108
c, 158.94 = 158.(32)4 = 158.38 = 458
d, 272.253 = (33)2.(52)3 = 36.56 = 156
a) $3^8:3^6=3^{8-6}=3^2$
$19^7:19^3=19^{7-3}=19^4$
$2^{10}:8^3=2^{10}:(2^3)^3=2^{10}:2^9=2^{10-9}=2^1$
$12^7:6^7=(12:6)^7=2^7$
$27^5:81^3=(3^3)^5:(3^4)^3=3^{15}:3^{12}=3^{15-12}=3^3$
b) $10^6:10=10^{6-1}=10^5$
$5^8:25^2=5^8:(5^2)^2=5^8:5^4=5^{8-4}=5^4$
$4^9:64^2=4^9:(4^3)^2=4^9:4^6=4^{9-6}=4^3$
$2^25:32^4=2^{25}:(2^5)^4=2^{25}:2^{20}=2^{25-20}=2^5$
$18^3:9^3=(18:9)^3=2^3$
\(\cdot3^8:3^6=3^{8-6}=3^2\)
\(\cdot19^7:19^3=19^{7-3}=19^4\)
\(\cdot2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^9=2\)
\(\cdot12^7:6^7=\left(12:6\right)^7=2^7\)
\(\cdot27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)
\(\cdot10^6:10=10^{6-1}=10^5\)
\(\cdot5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^4=5^4\)
\(\cdot4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^6=4^3\)
\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^5\)
\(18^3:9^3=\left(18:9\right)^3=2^3\)
a) \(2^5\cdot8^4\\ =2^5\cdot\left(2^3\right)^4\\ =2^5\cdot2^{12}\\ =2^{17}\)
b) \(25^6\cdot125^3\\ =\left(5^2\right)^6\cdot\left(5^3\right)^3\\ =5^{12}\cdot5^9\\ =5^{21}\)
c) \(625^3:25^7\\ =\left(5^4\right)^3:\left(5^2\right)^7\\ =5^{12}:5^{14}\\ =5^{-2}=\frac{1}{5^2}\)
d) \(4^{10}\cdot2^{30}\\ =\left(2^2\right)^{10}\cdot2^{30}\\ =2^{20}\cdot2^{30}\\= 2^{50}\)
e) \(9^{25}\cdot27^4\cdot81^3\\ =\left(3^2\right)^{25}\cdot\left(3^3\right)^4\cdot\left(3^4\right)^3\\ =3^{50}\cdot3^{12}\cdot3^{12}\\ =3^{74}\)
Viết biểu thức dưới dạng một lũy thừa:
a,410*815
=(2^2)^10 x (2^3)^15
=2^20 x 2^45
=2^65
Bài 1 :
a) \(\left(2^{17}+17^2\right).\left(9^{15}-3^{15}\right).\left(2^4-4^2\right)\)
\(=\left(2^{17}+17^2\right).\left(9^{15}-3^{15}\right).\left(16-16\right)\)
\(=\left(2^{17}+17^2\right).\left(9^{15}-3^{15}\right).0\)
\(=0\)
câu b sai đề rồi bạn , mình sủa lại đề nha :
b) \(\left(8^{2017}-8^{2015}\right)\div\left(8^{2014}.8\right)\)
\(=\left(8^{2017}-8^{2015}\right)\div8^{2015}\)
\(=8^{2017}\div8^{2015}-8^{2015}\div8^{2015}\)
\(=8^2-1\)
\(=64-1\)
\(=63\)
c) \(\left(1^3+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left(3^8-81^2\right)\)
\(=\left(1^3+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left[3^8.\left(3^4\right)^2\right]\)
\(=\left(1^3+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left[3^8-3^8\right]\)
\(=\left(1^3+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).0\)
\(=0\)
d) \(\left(2^8+8^3\right)\div\left(2^5.2^3\right)\)
\(=\left[2^8+\left(2^3\right)^3\right]\div2^8\)
\(=\left[2^8+2^9\right]\div2^8\)
\(=2^8\div2^8+2^9\div2^8\)
\(=1+2\)
\(=3\)
Bài 2 :
a) \(125^5\div25^3=\left(5^3\right)^5\div\left(5^2\right)^3=5^{15}\div5^6=5^9\)
b) \(27^6\div9^3=\left(3^3\right)^6\div\left(3^2\right)^3=3^{18}\div3^6=3^{12}\)
c) \(4^{20}\div2^{15}=\left(2^2\right)^{20}\div2^{15}=2^{40}\div2^{15}=2^{25}\)
d) \(24^n\div2^{2n}=24^n\div4^n=6^n\)
(32)25.(33)4.(34)3=350.312.312=374
(52)50.(53)5=5115
(416)3.48.(42)4=
a 350 x312 x 312 = 374
b 5100 x 515 =5115
c 49 x 48 x 48 = 425
Trả lời
a)58:52=56
b)37:34=33
c)274:95=(33)4:(32)5=312:310=32
Bài 2:
a)n=4
b)n=3
c)n=2
d)n=4
a125^5:25^3=(5^3)^5:(5^2)^3=5^15:5^6=5^9
b27^6:9^3=(3^3)^6:(3^2)^3=3^18:3^6=3^13
c 4^20:2^15=(2^2)^20:2^15=2^40:2^15=2^25
d24^n:2^2.n=24^n:(2^2)^n=24^n:4^n=(24:4)^n=6^n
e 64^4 . 16^5:4^20=(2^6)^4 . (2^4)^5 :(2^2)^20=2^24 . 2^20:2^40=2^4
g 32^4:8^6=(2^5)^4:(2^3)^6=2^20:2^18=2^2
a, \(125^5:25^3=\left(5^3\right)^5:\left(5^2\right)^3=5^{15}:5^6=5^9\)
b, \(27^6:9^3=\left(3^3\right)^6:\left(3^2\right)^3=3^{18}:3^6=3^{12}\)
c, \(4^{20}:2^{15}=\left(2^2\right)^{20}:2^{15}=2^{40}:2^{15}=2^{25}\)
d, \(24^n:2^{2.n}=2^n.12^n:2^n.2^n=12^n:2^n=2^n.6^n:2^n=6^n\)
e, \(64^4.16^5:4^{20}=4^{12}.4^{10}:4^{20}=4^{12+10-20}=4^2\)
g, \(32^4:8^6=8^4.4^4:8^4.8^2=4^4:4^2.2^2=4^2.2^2=2^4.2^2=2^6\)