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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 1:
a) 510 : 57 - 25 . 30 = 53- 25= 125 - 32= 93
b) \(\frac{2^{14}\cdot14\cdot125}{35^3\cdot6}=\frac{2^{14}\cdot2\cdot7\cdot5^3}{\left(7\cdot5\right)^3\cdot2\cdot3}=\frac{2^{15}\cdot7\cdot5^3}{7^3\cdot5^3\cdot2\cdot3}=\frac{2^{14}}{7^2\cdot3}=\frac{16384}{49\cdot3}=\frac{16384}{174}\)
c) \(\frac{2^{13}+2^5}{2^{10}+2^2}=\frac{2^{11}\cdot2^2+2^3\cdot2^2}{2^2\cdot2^8+2^2}=\frac{2^2\left(2^{11}+2^3\right)}{2^2\left(2^8+1\right)}=\frac{2^{11}+2^3}{2^8+1}=\frac{2^3\cdot2^8+2^3}{2^8+1}=\frac{2^3\left(2^8+1\right)}{2^8+1}=2^3=8\)
Bài 2:
a) 59 . 252 = 59 . (52)2= 59 . 54= 513
b) 1410 : 495 = [(2.7)10] : [(7.7)5] = (210 . 710 ) : (75 . 75) = 210 . 710 : 710= 210
c) 414 . 528 = (22)14 . 528 = 228 . 528 = (2.5)28 = 1028
d) 10010 : (-10)3 . (-100)4 = (102)3 : 103.(-1) . (102)4= 106 : 103 . 108 .(-1) = -1011
Trả lời:
Ta có : 1.22= 1.2.2=1.2.(3-1)=1.2.3-1.2
2.32= 2.3.3=2.3.(4-1)=2.3.4-2.3
.................................................
98.992= 98.99.99=98.99.(100-1)=98.99.100-98.99
A=1.2.3 - 1.2 + 2.3.4 - 2.3 + ... + 98.99.100 - 98.99 hay A=1.2.3 + 2.3.4 +...+ 98.99.100 - (1.2 + 2.3 + ... + 98.99) = B - C
B=1.2.3 + 2.3.4 + ... + 98.99.100
B.4=1.2.3.4 + 2.3.4.(5 - 1) + ... + 98.99.100.(101 - 97)= 98.99.100.101
=> 98.99.100.101:4= 24497550
C=1.2 + 2.3 + ... + 98.99
C.3=1.2.3 + 2.3.(4 - 1) + ... + 98.99.(100 - 97)= 98.99.100
=> 98.99.100:3= 323400
Vậy A= 24497550 - 323400 = 24174150
a) Ta có :
164 = ( 42 )4 = 48 < 411
=> 164 < 411
b) Ta có :
8115 = ( 92 )15 = 930 > 920
=> 8115 > 920
c) Ta có :
250 = ( 25 )10 = 3210 > 2510 = ( 52 )10 = 520
=> 250 > 520
d) Ta có :
545 = ( 53 )15 = 12515 > 12115 = ( 112 )15 = 1130
=> 545 > 1130
e) Ta có :
7300 = ( 72 )150 = 49150 < 64150 = ( 43 )150 = 4450
=> 7300 < 4450
mk sẽ tíck cho những bn trả lời cho mk( nhank giúp mk, mk cần gấp!)
\(\frac{x+1}{3}=\frac{9}{2}\)
\(\left(x+1\right).2=9.3\)
\(\left(x+1\right).2=27\)
\(x+1=27:2\)
\(x+1=13,5\)
\(x=13,5-1=12,5\)
vậy x = 12.5
\(\frac{x+1}{3}=\frac{9}{2}\)
\(\Leftrightarrow2\left(x+1\right)=3\times9\)
\(\Leftrightarrow2\left(x+1\right)=27\)
\(\Leftrightarrow x+1=\frac{27}{2}\)
\(\Leftrightarrow x=\frac{25}{2}\)