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244.34-3212:1612
=(24.3)4-(32:16)12
=724-212
=26873856-4096
=26869760.
B1:
Ta có: \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}-2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}-2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1-5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}\)
\(=\frac{2.\left(-4\right)}{3.5}=-\frac{8}{15}\)
B2:
Ta có: \(1+3+5+...+x=1600\)
\(\Leftrightarrow\frac{\left(x+1\right)\cdot\left(\frac{x-1}{2}+1\right)}{2}=1600\)
\(\Leftrightarrow\left(x+1\right)\cdot\frac{x+1}{2}=3200\)
\(\Leftrightarrow\left(x+1\right)^2=6400\)
Xét theo dãy tăng tiến ta thấy được giá trị của x càng tăng
=> x dương => x + 1 dương
\(\Rightarrow x+1=80\)
\(\Rightarrow x=79\)
\(A=1+6+6^2+...+6^{100}\)
\(6A=6+6^2+6^3+...+6^{101}\)
\(6A-A=\left(6+6^2+...+6^{101}\right)-\left(1+6+...+6^{100}\right)\)
\(5A=6^{101}-1\)
\(A=\frac{6^{101}-1}{5}\)
Hoàn toàn tương tự với các câu b) c)
\(A=1+6+6^2+6^3+...+6^{100}\)
\(6A=6+6^2+6^3+6^4+...+6^{101}\)
\(6A-A=\left(6+6^2+6^3+6^4+...+6^{101}\right)-\left(1+6+6^2+...+6^{100}\right)\)
\(5A=6^{101}-1\)
\(A=\frac{6^{101}-1}{5}\)
\(A=\frac{9^{14}.25^5.8^7}{18^{12}.625^{324}.24^3}\)
\(A=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{2^{12}.9^{12}.\left(5^4\right)^{324}.3^3.8^3}\)
\(A=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.\left(3^2\right)^{12}.5^{1296}.3^3.\left(2^3\right)^3}\)
\(A=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{24}.5^{1296}.3^3.2^9}\)
\(A=\frac{3^{28}.5^{10}.2^{21}}{2^{30}.3^{27}.5^{1296}}\)
\(A=\frac{3}{2^9.5^{1286}}\)
a) 5 + ( -12 ) - 10
= -7 - 10
= -17
b) 25 - ( -17 ) + 24 - 12
= 25 + 17 + 24 - 12
= 42 + 24 - 12
= 66 - 12
= 54
c) 56 : 54 + 23 . 22 - 225 : 152
= 56 - 4 + 23 + 2 - 32 . 52 : 152
= 52 + 25 - 152 : 152
= 25 + 32 - 1
= 57 - 1
= 56
d) ( -5 - 3 ) . ( 3 - 5 ) : ( -3 + 5 )
= ( -8 ) . ( -2 ) : 2
= -8 . [ ( -2 ) : 2 ]
= -8 . ( -1 )
= 8
a) 5 + ( -12) - 10
= 5 - 12 -10
= -17
b) 25 - ( -17) + 24 - 12
= 25 + 17 + 24 - 12
= 42 + 24 - 12
= ( 42 - 12) + 24
= 30 + 24 = 54
c) 56 : 54 + 23 . 22 - 225 : 152
= 52 + 25 - 1
= 25 + 32 - 1
= 56
d) ( - 5 - 3) . ( 3 - 5) : ( -3 + 5)
= ( -8) . ( -2) : 2
= 16 : 2
= 8
\(B=\frac{4^6.3^4.9^5}{6^{12}}=\frac{\left(2^2\right)^6.3^4.\left(3^2\right)^5}{\left(2.3\right)^{12}}=\frac{2^{12}3^4.3^{10}}{2^{12}.3^{12}}=\frac{3^{14}}{3^{12}}=3^2=9.\)
\(B=\frac{4^6.3^4.9^5}{6^{12}}\)
\(B=\frac{\left(2^2\right)^6.3^4.\left(3^2\right)^5}{\left(2.3\right)^{12}}\)
\(B=\frac{2^{12}.3^4.3^{10}}{2^{12}.3^{12}}\)
\(B=\frac{2^{12}.3^{14}}{2^{12}.3^{12}}\)
\(B=3^2=9\)
~~Hok tốt~~
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