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9 tháng 9
\(1)2^8:2^4+3^2\cdot3=2^4+3^3=16+27=43\)
\(2)3^{24}:3^{21}+2^2\cdot2^3=3^3+2^5=27+32=59\)
\(3)5^9:5^7+12\cdot3+7^0=5^2+36+1=25+37=62\)
\(4)5^6:5^4+3^2-2021^0=5^2+3^2-1=25+9-1=33\)
\(5)3^{19}:3^{16}+5^2\cdot2^3-1^{2021}=3^3+25\cdot8-1=27+200-1=226\)
\(6)3^6:3^5+2\cdot2^3+2021^0=3^1+2^4+1=3+16+1=20\)
9 tháng 9
1: \(1026-\left\lbrack\left(3^4+1\right):41\right\rbrack\)
\(=1026-82:41\)
=1026-2
=1024
\(2^{11}:\left\lbrace1026-\left\lbrack\left(3^4+1\right):41\right\rbrack\right\rbrace\)
\(=2^{11}:2^{10}=2\)
2: \(250:\left\lbrace1500:\left\lbrack4\cdot5^3-2^3\cdot25\right\rbrack\right\rbrace\)
\(=250:\left\lbrace1500:\left\lbrack4\cdot125-8\cdot25\right\rbrack\right\rbrace\)
\(=250:\left\lbrace1500:\left\lbrack500-200\right\rbrack\right\rbrace=250:\frac{1500}{3}=250:500=0,5\)
3: \(12+3\cdot\left\lbrace90:\left\lbrack39-\left(2^3-5\right)^2\right\rbrack\right\rbrace\)
\(=12+3\cdot\left\lbrace90:\left\lbrack39-\left(8-5\right)^2\right\rbrack\right\rbrace\)
\(=12+3\cdot\left\lbrace90:\left\lbrack39-3^2\right\rbrack\right\rbrace\)
\(=12+3\cdot\left\lbrace90:\left\lbrack39-9\right\rbrack\right\rbrace\)
\(=12+3\cdot\left\lbrace90:30\right\rbrace=12+3\cdot3=21\)
4: \(24:\left\lbrace390:\left\lbrack500-\left(5^3+49\cdot5\right)\right\rbrack\right\rbrace\)
\(=24:\left\lbrace390:\left\lbrack500-\left(125+245\right)\right\rbrack\right\rbrace\)
\(=24:\left\lbrace390:\left\lbrack500-125-245\right\rbrack\right\rbrace\)
\(=24:\left\lbrace390:\left\lbrack375-245\right\rbrack\right\rbrace\)
\(=24:\left\lbrace390:130\right\rbrace=\frac{24}{3}=8\)
5: \(117:\left\lbrace\left\lbrack79-3\cdot\left(3^3-17\right)\right\rbrack:7+2\right\rbrace\)
\(=117:\left\lbrace\left\lbrack79-3\cdot\left(27-17\right)\right\rbrack:7+2\right\rbrace\)
\(=117:\left\lbrace\left\lbrack79-3\cdot10\right\rbrack:7+2\right\rbrace\)
\(=117:\left\lbrace49:7+2\right\rbrace=\frac{117}{9}=13\)
6: \(514-4\cdot\left\lbrace\left\lbrack40+8\left(6-3\right)^2\right\rbrack-12\right\rbrace\)
\(=514-4\cdot\left\lbrace\left\lbrack40+8\cdot3^2\right\rbrack-12\right\rbrace\)
\(=514-4\cdot\left\lbrace\left\lbrack40+8\cdot9\right\rbrack-12\right\rbrace\)
\(=514-4\cdot\left\lbrace112-12\right\rbrace\)
\(=514-4\cdot100=514-400=114\)
7: \(25\cdot\left\lbrace32:\left\lbrack\left(12-4\right)+4\cdot\left(16:2^3\right)\right\rbrack\right\rbrace\)
\(=25\cdot\left\lbrace32:\left\lbrack8+4\cdot2\right\rbrack\right\rbrace\)
\(=25\cdot\left\lbrace32:16\right\rbrace=25\cdot2=50\)
8: \(30:\left\lbrace175:\left\lbrack355-\left(135+37\cdot5\right)\right\rbrack\right\rbrace\)
\(=30:\left\lbrace175:\left\lbrack355-\left(135+185\right)\right\rbrack\right\rbrace\)
\(=30:\left\lbrace175:\left\lbrack355-320\right\rbrack\right\rbrace=30:\left\lbrace175:35\right\rbrace=\frac{30}{5}=6\)
9: \(32:\left\lbrace160:\left\lbrack300-\left(175+21\cdot5\right)\right\rbrack\right\rbrace\)
\(=32:\left\lbrace160:\left\lbrack300-\left(175+105\right)\right\rbrack\right\rbrace\)
\(=32:\left\lbrace160:\left\lbrack300-280\right\rbrack\right\rbrace\)
\(=32:\left\lbrace160:20\right\rbrace=\frac{32}{8}=4\)
10: \(750:\left\lbrace130-\left\lbrack\left(5\cdot14-65\right)^3+3\right\rbrack\right\rbrace\)
\(=750:\left\lbrace130-\left\lbrack\left(70-65\right)^3+3\right\rbrack\right\rbrace\)
\(=750:\left\lbrace130-\left\lbrack5^3+3\right\rbrack\right\rbrace\)
\(=750:\left\lbrace130-128\right\rbrace=750:2=375\)
9 tháng 9
1: \(3^2\cdot5^3+9^2\)
\(=9\cdot125+81\)
=1125+81
=1206
2: \(55+45:3^2\)
\(=55+45:9\)
=55+5
=60
3: \(8^3:4^2-5^2=64:16-25=4-25=-21\)
4: \(5\cdot3^2-32:2^2=5\cdot9-32:4=45-8=37\)
5: \(16:2^3+5^2\cdot4=16:8+25\cdot4\)
=2+100
=102
6: \(5\cdot2^2-18:3^2\)
\(=5\cdot4-18:9\)
=20-2
=18
7: \(3\cdot5^2-15\cdot2^2=3\cdot25-15\cdot4=75-60=15\)
8: \(2^3\cdot6-72:3^2=8\cdot6-72:9=48-8=40\)
9: \(5\cdot2^2-27:3^2\)
\(=5\cdot4-27:9\)
=20-3
=17
10: \(3\cdot2^4+81:3^2=3\cdot16+81:9=48+9=57\)
11: \(4\cdot5^3-32:2^5=4\cdot125-32:32=500-1=499\)
12: \(6\cdot5^2-32:2^4=6\cdot25-32:16=150-2=148\)
Ta có: \(F=5+5^3+5^5+\cdots+5^{101}\)
=>\(25F=5^3+5^5+5^7+\cdots+5^{103}\)
=>\(25F-F=5^3+5^5+5^7+\cdots+5^{103}-5-5^3-5^5-\cdots-5^{101}\)
=>\(24F=5^{103}-5\)
=>\(F=\frac{5^{103}-5}{24}\)
Ta có: \(5^{103}+1>5^{103}-5\)
=>\(\frac{5^{103}+1}{24}>\frac{5^{103}-5}{24}\)
=>E>F