a, A=(7-9)mũ 3 +(-5)mũ 7 :(-5) mũ 5 +2010 mũ 0
b, B=[2.(-2) mũ 2 +1:(-3) mũ 2] + 9.7 - (-2) mũ 6
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a) \(A=2^1+2^2+2^3+2^4+...+2^{2010}\)
\(A=\left(2^1+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{2009}+2^{2010}\right)\)
\(A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{2009}\left(1+2\right)\)
\(A=3\left(2+2^3+...+2^{2009}\right)⋮3\)
\(A=2^1+2^2+2^3+2^4+...+2^{2010}\)
\(A=\left(2^1+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{2008}+2^{2009}+2^{2010}\right)\)
\(A=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{2008}\left(1+2+2^2\right)\)
\(A=7\left(2^1+2^4+...+2^{2008}\right)⋮7\)
Các ý dưới bạn làm tương tự nhé.
*Ta có: A\(=2^1+2^2+2^3+2^4+...+2^{2010}\)
\(=\left(2+2^2\right)+2^2\times\left(2+2^2\right)+...+2^{2008}\times\left(2+2^2\right)\)
\(=\left(2+2^2\right)\times\left(1+2^2+2^3+...+2^{2008}\right)\)
\(=6\times\left(2^2+2^3+...+2^{2008}\right)\)
\(=3\times2\times\left(2^2+2^3+...+2^{2008}\right)\)
\(\Rightarrow A⋮3\)
*Ta có: A \(=2^1+2^2+2^3+2^4+...+2^{2010}\)
\(=2\times\left(1+2+2^2\right)+2^4\times\left(1+2+2^2\right)+...+2^{2008}\times\left(1+2+2^2\right)\)
\(=\left(1+2+2^2\right)\times\left(2+2^4+2^7+...+2^{2008}\right)\)
\(=7\times\left(2+2^4+2^7+...+2^{2008}\right)\)
\(\Rightarrow A⋮7\)
Mình sửa lại đề C 1 chút xíu
*Ta có: C \(=3^1+3^2+3^3+3^4+...+3^{2010}\)
\(=\left(3+3^2\right)+3^2\times\left(3+3^2\right)+...+3^{2008}\times\left(3+3^2\right)\)
\(=\left(3+3^2\right)\times\left(1+3^2+3^3+...+3^{2008}\right)\)
\(=12\times\left(1+3^2+3^3+...+3^{2008}\right)\)
\(=4\times3\times\left(1+3^2+3^3+...+3^{2008}\right)\)
\(\Rightarrow C⋮4\)
Các câu khác làm tương tự nhé. Chúc bạn học tốt!
1; 73.52.54.76:(55.78)
= (73.76).(52.54) : (55.78)
= 79.56: (55.78)
= (79:78).(56:55)
= 7.5
= 35
2; 33.a7.3.a2:(34.a6)
= (33.3).(a7.a2): (34.a6)
= 34.a9: (34.a6)
= (34:34).(a9:a6)
= a3
a,\(5^3.2-100:4+2^3.5\)
= 125 . 2 - 25 + 8 . 5
= 250 - 25 + 40
= 265
b, \(6^2:9+50.2-3^3.3\)
= 36 : 9 + 100 - 27 . 3
= 4 + 100 - 81
= 23
a) \(2^3.3^2=8.9=72\)
b) \(5^{10}:5^7=5^2=25\)
c) \(2^6:2=2^5=32\)
d) \(7^4:7^4=7^0=1\)
e) \(9^5:9^5=9^0=1\)
a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)
`#3107.101107`
\(3^9\div3^8+5^8\div5^7\\ =3^{9-8}+5^{8-7}\\ =3+5\\ =8\)
_______
\(6^9\div6^7-30\\ =6^{9-7}-30\\ =6^2-30\\ =36-30\\ =6\)
________
\(\left(2^7\times2^2\right)\div2^9-5^0\\ =2^{7+2}\div2^9-1\\ =2^9\div2^9-1\\ =2^0-1\\ =1-1\\ =0\)
_______
\(3\times3\times3\times3\times3\times3^5\\ =3^{1+1+1+1+1+5}\\ =3^{10}\)
a) A = (7-9)3+ (-5)7 :(-5)5 +20100=(-2)3 + (-5)7-5 +1
=-8 +(-5)2 +1 = -8 +25 +1=18
B) b=(2.(-2)2 +1:(-3)2) +9.7 -(-2)6 =2.4 +1/9 + 63 - 64 = 8 +1/9 -1 =64/9
CHÚC BN GIỎI NHÉ <3