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: \(6\cdot5^2-32:2^4=6\cdot25-32:16=150-2=148\)

Giúp mình với mng ơi!!

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: \(750:\left\lbrace130-\left\lbrack\left(5\cdot14-65\right)^3+3\right\rbrack\right\rbrace\)

\(=750:\left\lbrace130-\left\lbrack\left(70-65\right)^3+3\right\rbrack\right\rbrace\)

\(=750:\left\lbrace130-\left\lbrack5^3+3\right\rbrack\right\rbrace\)

\(=750:\left\lbrace130-128\right\rbrace=750:2=375\)

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

Bài 7: Ta có: \(a\cdot b=ƯCLN\left(a;b\right)\cdot BCN\mathbb{N}\left(a;b\right)\)

=>\(a\cdot b=10\cdot900=9000\)

ƯCLN(a;b)=10

=>a⋮10; b⋮10

ab=9000

mà a⋮10 và b⋮10 và a<b

nên (a;b)∈{(10;900);(20;450);(30;300);(50;180);(60;150);(90;100)}

mà ƯCLN(a;b)=10

nên (a;b)∈{(10;900);(20;450);(50;180);(90;100)}

Bài 5:

ƯCLN(a;b)=6

=>a⋮6; b⋮6

ab=216

mà a⋮6; b⋮6

nên (a;b)∈{(6;36);(12;18);(18;12);(36;6)}

Bài 4: Gọi hai số tự nhiên cần tìm là a,b

ƯCLN(a;b)=5

=>a⋮5; b⋮5

Ta có: ab=300

mà a⋮5; b⋮5

nên (a;b)∈{(5;60);(60;5);(10;30);(30;10);(15;20);(20;15)}

Bài 1:

a: ƯCLN(a;b)=6

=>a⋮6 và b⋮6

a+b=96

mà a⋮6 và b⋮6

nên (a;b)∈{(6;90);(90;6);(12;84);(84;12);(18;78);(78;18);(24;72);(72;24);(30;66);(66;30);(36;60);(60;36);(42;54);(54;42);(48;48)}

mà ƯCLN(a;b)=6

nên (a;b)∈{(6;90);(90;6);(18;78);(78;18);(30;66);(66;30);(42;54);(54;42)}

b: ƯCLN(a;b)=4

=>a⋮4 và b⋮4

a+b=16

mà a⋮4; b⋮4 và a>b

nên (a;b)∈{(12;4);(8;8)}

mà ƯCLN(a;b)=4

nên (a;b)=(12;4)

ngón tay gầy

Trả lời gúp mình với p

d: \(48\cdot26+24\cdot148\)

\(=48\cdot26+48\cdot74\)

\(=48\cdot\left(26+74\right)=48\cdot100=4800\)

e: \(23\cdot48+92\cdot88\)

\(=23\cdot4\cdot12+92\cdot88\)

\(=92\cdot12+92\cdot88=92\cdot100=9200\)

b: \(89\cdot25+89\cdot74+89\)

\(=89\cdot\left(25+74+1\right)\)

\(=89\cdot100=8900\)