Bài 1: Dùng tính chất của các phép toán để tinh nhanh
17.25
2^3.2^2+5^5:5^3
29.31+ 66.69+31.37
Bài 2: Tìm x, biết
x+ 3^2.3=7^5:7^3
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1: =-3x5+2x5-7x5+7x4=-8x5+7x4=-40+28=-12
2: =-3x5+3x6-4x3+4x2=-9+8=-1
3: =17(-84-16)=-1700
4: =1975(-115+15)=-197500
5: =-145x13+145x57+57x10-57x145=-1315
1/ \(5\left(-3+2\right)-7\left(5-4\right)\)
\(=5.\left(-3\right)+5.2-7.5-7.\left(-4\right)\)
\(=-15+10-35+28\)
\(=-5-7\)
\(=-12\)
2/ \(3.\left(-5+6\right)-4.\left(3-2\right)\)
\(=3.\left(-5\right)+3.6-4.3-4.\left(-2\right)\)
\(=-15+18-12+8\)
\(=3-4\)
\(=-1\)
3/ \(17.\left(-84\right)+17.\left(-16\right)\)
\(=17.\left(-84-16\right)\)
\(=17.\left(-100\right)\)
\(=-1700\)
4/ \(1975.\left(-115\right)+1975.15\)
\(=1975.\left(-115+15\right)\)
\(=1975.\left(-100\right)\)
\(=-197500\)
5/ \(-145.\left(13-57\right)+57.\left(10-145\right)\)
\(=-145.13-145.\left(-57\right)+57.10+57.\left(-145\right)\)
\(=-145.\left(-57+57\right)-145.13+57.10\)
\(=0-1885+570\)
\(=-1315\)
6/ \(157.17-157.7\)
\(=157.\left(17-7\right)\)
\(=157.10\)
\(=1570\)
7/ \(199.\left(15-17\right)-199.\left(-17+5\right)\)
\(=199.\left(-2\right)-199.\left(-12\right)\)
\(=199.\left(-2\right)+199.12\)
\(=199.\left(-2+12\right)\)
\(=199.10\)
\(=1990\)
8/ \(-39.\left(5-99\right)+99.\left(10-39\right)\)
\(=-39.5-39.\left(-99\right)+99.10+99.\left(-39\right)\)
\(=-39.\left(-99+99\right)-39.5+99.10\)
\(=0-195+990\)
\(=795\)
9/ \(-38.\left(25-4\right)+25.\left(-4+38\right)\)
\(=-38.25-38.\left(-4\right)+25.\left(-4\right)+25.38\)
\(=25.\left(-38+38\right)-4.\left(-38+25\right)\)
\(=0-4.\left(-13\right)\)
\(=52\)
10/ \(\left(-37\right).86+37.76\)
\(=37.\left(-86\right)+37.76\)
\(=37.\left(-86+76\right)\)
\(=37.\left(-10\right)\)
\(=-370\)
2) -3(4 - 7) + 5(-3 + 2)
= -3.4 + 3.7 - 5.3 + 5.2
= -12 + 21 -15 + 10
= 31 - 27
= 4
4) -5(2 - 7) + 4(2 - 5)
= -5.2 + 5.7 + 4.2 - 4.5
= -10 + 35 + 8 - 20
= 38 - 30
= 8
3: \(=20-12-8+12=20-8=12\)
5: \(=-18-42-21-35=-116\)
3: \(=-15+18-12+8=-27+26=-1\)
2: \(=-12+21-15+10=9-5=4\)
a. (15+3)/2+(2+3)^3*5
b.(5+3)^4*2+(21+7)/3
c. 7^6/3+(5+6)*2
d. 5^2*3^3+(4+2)*2%
a) \(5^{n+3}-5^{n+1}=5^{12}.120\Leftrightarrow5^{n+1}.\left(5^2-1\right)=5^{12}.5.24\)
\(\Leftrightarrow24.5^{n+1}=5^{13}.24\Leftrightarrow5^{n+1}=5^{13}\Leftrightarrow n+1=13\Leftrightarrow n=12\)
b) \(2^{n+1}+4.2^n=3.2^7\)
\(\Leftrightarrow2^n\left(2+4\right)=3.2^7\Leftrightarrow6.2^n=3.2^7\Leftrightarrow2^n=2^6\Leftrightarrow n=6\)
c) \(3^{n+2}-3^{n+1}=486\)
\(\Leftrightarrow3^{n+1}.\left(3-1\right)=486\Leftrightarrow2.3^{n+1}=486\Leftrightarrow3^{n+1}=243\)
\(\Leftrightarrow3^n=243:3=81=3^3\Leftrightarrow n=3\)
d) \(3^{2n+3}-3^{2n+2}=2.3^{10}\)
\(\Leftrightarrow3^{2n+2}.\left(3-1\right)=2.3^{10}\)
\(\Leftrightarrow3^{2n+2}.2=2.3^{10}\Leftrightarrow3^{2n+2}=3^{10}\Leftrightarrow2n+2=10\Leftrightarrow2n=8\Leftrightarrow n=4\)
\(2+\dfrac{3}{4}=\dfrac{8}{4}+\dfrac{3}{4}=\dfrac{11}{4}\\ \dfrac{5}{7}:6=\dfrac{5}{7}\times\dfrac{1}{6}=\dfrac{5}{42}\\ 2-\dfrac{3}{5}=\dfrac{10}{5}-\dfrac{3}{5}=\dfrac{7}{5}\\ \dfrac{5}{9}\times\dfrac{2}{7}=\dfrac{10}{63}\)
\(2^3.2^2+5^5:5^3\)
\(=2^5+5^2\)
\(=32+25\)
\(=57\)
Bài 1 a, \(17.25\)
\(=\left(1+16\right).25\)
\(=1.25+16.25\)
\(=25+4.4.25\)
\(=25+4.100\)
\(=25+400\)
\(=425\)
b, Bạn kia làm rồi nhé!
c, \(29.31+66.69+31.37\)
\(=31.\left(29+37\right)+66.99\)
\(=31.66+66.69\)
\(=66\left(31+69\right)\)
\(=66.100\)
\(6600\)