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a) \(\left(3^5\times3^7\right):3^{10}+5\times2^4-7^3:7=3^{12}:3^{10}+5\times2^4-7^2\)
\(=3^2-5\times16-7^2=9-80-49=-120\)
b) \(15:\left(3^5:3^4\right)-2^9:2^7=15:3-2^2=5-4=1\)
c)\(5\times3^5:\left(3^8:3^5\right)-2^3\times5=5\times3^5:3^3-2^3\times5\)
\(=5\times3^2-2^3\times5=5\times9-8\times5=45-40=5\)
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a) 25 : 23
C1: 25 : 23
= 32 : 8
= 4
C2: 25 : 23
= 25 - 3
= 22 = 4
b) 35 : 32
C1: 35 : 32
= 243 : 9
= 27
C2: 35 : 32
= 35 - 2
= 33 = 27
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Câu 1 :
\(A=5+5^2+5^3+......+5^{2016}\)( 1 )
\(A.5=5^2+5^3+5^4+.....+5^{2017}\)( 2 )
Lấy ( 2 ) - ( 1 ) ta được :
\(A.5-A=\left(5^2+5^3+5^4+......+5^{2017}\right)-\left(5+5^2+5^3+......+5^{2016}\right)\)
\(A.4=5^{2017}-5\)
\(A=\left(5^{2017}-5\right):4\)
\(\Rightarrow4A+5=\left(5^{2017}-5\right):4.4\)
\(\Rightarrow4A+5=5^{2017}-5\)
Câu 2 :
\(A=7+7^2+7^3+.....+7^{2016}\)( 1 )
\(A.7=7^2+7^3+7^4+......+7^{2017}\)( 2 )
Lấy ( 2 ) - ( 1 ) ta được :
\(A.7-A=\left(7^2+7^3+7^4+.....+7^{2017}\right)-\left(7+7^2+7^3+.....+7^{2016}\right)\)
\(A.6=7^{2017}-7\)
\(A=\left(7^{2017}-7\right):6\)
\(\Rightarrow6.A+7=\left(7^{2017}-7\right):6.6\)
\(\Rightarrow6.A+7=7^{2017}-7\)
Câu 1:
\(A=5+5^2+5^3+......+5^{2016}\)
\(5A=5^2+5^3+5^4+.......+5^{2017}\)
\(\Rightarrow5A-A=\left(5^2+5^3+5^4+.......+5^{2017}\right)-\left(5+5^2+5^3+.......+5^{2016}\right)\)
\(\Rightarrow5A-A=5^2+5^3+5^4+.........+5^{2017}-5-5^2-5^3-........-5^{2016}\)
\(\Rightarrow4A=5^{2017}-5\)
\(\Rightarrow4A+5=5^{2017}\)
Câu 2 tương tự câu 1
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