\(4^{15}.5^{30}=\left(2^2\right)^{15}.5^{30}=2^{30}.5^{30}=\left(2.5\right)^{30}=10^{30}\)

\(27^{16}.9^{10}=\left(3^3\right)^{16}.\left(3^2\right)^{10}=3^{48}.3^{20}=3^{68}\)

\(\frac{72^3.54^2}{1084}=\frac{\left(2^3.3^2\right)^3.\left(2.3\right)^2}{2^2.271}=\frac{2^2.2^9.3^6.3^2}{2^2.271}=\frac{2^9.3^8}{271}\)

\(\frac{3^{10}.11+3^{10}.5}{39.24}=\frac{3^{10}.16}{39.24}=\frac{3.3.3^8.2.8}{3.13.3.8}=\frac{3^8.2}{13}\)(Cái này đoán đề thoi, thật sự câu này viết đề chả hiểu gì)

(^) cái này là mủ í bn

`a)5/8x+2/5=1/5`

`=>5/8x=1/5-2/5`

`=>5/8x=-1/5`

`=>x=-1/5:5/8=-8/25`

`b)5/7:x+11/7=18/7`

`=>5/7:x=18/7-11/7`

`=>5/7:x=1`

`=>x=5/7`

`c)(-1,2).(-3/24)+(0,4-1 4/15):1 2/3`

`=(-6/5).(-1/8)+(2/5-19/15):5/3`

`=3/20+(-13/15)*3/5`

`=3/20-13/25=-37/100`

a)5/8.x+2/5=1/5

5/8.x=1/5 - 2/5

5/8.x=-1/5

x=(-1/5):5/8

x=(-1/5).8/5

x=-8/25.      Vậy x=-8/25

b)5/7:x +11/7=18/7

5/7:x=1

x=5/7:1

x=5/7.      Vậy x=5/7

Vì \(x=19\) nên \(x-19=0\)

Ta có: A = \(x^5-20x^4+21x^3-39x^2+18x\)

= \(x^5-19x^4-x^4+19x^3+2x^3-38x^2-x^2+19x-x\)

= \(x^4\left(x-19\right)-x^3\left(x-19\right)+2x^2\left(x-19\right)-x\left(x-19\right)-x\)

= \(-x=-19\)

Bài này bạn có thể làm theo cách khác chẳng hạn bạn áp dụng đ/lí Bê-du rồi lập sơ đồ Hooc-ne để tính

a)\(\dfrac{2}{3}.\dfrac{4}{5}+\dfrac{1}{3}.\dfrac{4}{5}=\left(\dfrac{2}{3}+\dfrac{1}{3}\right).\dfrac{4}{5}=1.\dfrac{4}{5}=\dfrac{4}{5}\)

b)\(\dfrac{2}{3}.\dfrac{4}{5}-\dfrac{1}{3}.\dfrac{4}{5}=\left(\dfrac{2}{3}-\dfrac{1}{3}\right).\dfrac{4}{5}=\dfrac{1}{3}.\dfrac{4}{5}=\dfrac{4}{15}\)

a) \(\dfrac{2}{3}\times\dfrac{4}{5}+\dfrac{1}{3}\times\dfrac{4}{5}=\dfrac{4}{5}\times\left(\dfrac{2}{3}+\dfrac{1}{3}\right)=\dfrac{4}{5}\times1=\dfrac{4}{5}\)

b) \(\dfrac{2}{3}\times\dfrac{4}{5}-\dfrac{1}{3}\times\dfrac{4}{5}=\dfrac{4}{5}\times\left(\dfrac{2}{3}-\dfrac{1}{3}\right)=\dfrac{4}{5}\times\dfrac{1}{3}=\dfrac{4}{15}\)

c) \(\dfrac{1}{2}:\dfrac{3}{4}+\dfrac{1}{6}:\dfrac{3}{4}=\dfrac{1}{2}\times\dfrac{4}{3}+\dfrac{1}{6}\times\dfrac{4}{3}=\dfrac{4}{3}\times\left(\dfrac{1}{2}+\dfrac{1}{6}\right)=\dfrac{4}{3}\times\dfrac{2}{3}=\dfrac{8}{9}\)

d) \(\dfrac{1}{2}:\dfrac{3}{4}-\dfrac{1}{6}:\dfrac{3}{4}=\dfrac{1}{2}\times\dfrac{4}{3}-\dfrac{1}{6}\times\dfrac{4}{3}=\dfrac{4}{3}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)=\dfrac{4}{3}\times\dfrac{1}{3}=\dfrac{4}{9}\)

a) 

\(\Rightarrow\dfrac{47}{10}.x=\dfrac{1}{5}+\dfrac{2}{3}\)

\(\Rightarrow\dfrac{47}{10}.x=\dfrac{3}{15}+\dfrac{10}{15}\)

\(\Rightarrow\dfrac{47}{10}.x=\dfrac{13}{15}\)

\(\Rightarrow x=\dfrac{13}{15}:\dfrac{47}{10}\)

\(\Rightarrow x=\dfrac{13}{10}.\dfrac{10}{47}\)

\(\Rightarrow x=\dfrac{13}{47}\)

b)

\(\Rightarrow\dfrac{5}{7}:x=\dfrac{1}{6}-\dfrac{4}{5}\)

\(\Rightarrow\dfrac{5}{7}:x=\dfrac{5}{30}-\dfrac{24}{30}\)

\(\Rightarrow\dfrac{5}{7}:x=-\dfrac{19}{30}\)

\(\Rightarrow x=\dfrac{5}{7}:\left(-\dfrac{19}{30}\right)\)

\(\Rightarrow x=\dfrac{5}{7}.\left(-\dfrac{30}{19}\right)\)

\(\Rightarrow x=-\dfrac{150}{133}\)

d: \(\frac{x}{6}-\frac{2}{y}=\frac{1}{30}\)

=>\(\frac{x}{6}-\frac{1}{30}=\frac{2}{y}\)

=>\(\frac{5x-1}{30}=\frac{2}{y}\)

=>\(y\left(5x-1\right)=60\)

=>(5x-1;y)∈{(1;60);(60;1);(-1;-60);(-60;-1);(2;30);(30;2);(-2;-30);(-30;-2);(3;20);(20;3);(-3;-20);(-20;-3);(4;15);(15;4);(-4;-15);(-15;-4);(5;12);(12;5);(-5;-12);(-12;-5);(6;10);(10;6);(-6;-10);(-10;-6)}

=>(5x;y)∈{(2;60);(61;1);(0;-60);(-59;-1);(3;30);(31;2);(-1;-30);(-29;-2);(4;20);(21;3);(-2;-20);(-19;-3);(5;15);(16;4);(-3;-15);(-14;-4);(6;12);(13;5);(-4;-12);(-11;-5);(7;10);(11;6);(-5;-10);(-9;-6)}

=>(x;y)∈{(2/5;60);(61/5;1);(0;-60);(-59/5;-1);(3/5;30);(31/5;2);(-1/5;-30);(-29/5;-2);(4/5;20);(21/5;3);(-2/5;-20);(-19/5;-3);(1;15);(16/5;4);(-3/5;-15);(-14/5;-4);(6/5;12);(13/5;5);(-4/5;-12);(-11/5;-5);(7/5;10);(11/5;6);(-1;-10);(-9/5;-6)}

c: \(\frac{5}{x}-\frac{y}{3}=\frac16\)

=>\(\frac{5}{x}=\frac{y}{3}+\frac16=\frac{2y+1}{6}\)

=>x(2y+1)=30

=>(x;2y+1)∈{(1;30);(30;1);(-1;-30);(-30;-1);(2;15);(15;2);(-2;-15);(-15;-2);(3;10);(10;3);(-3;-10);(-10;-3);(5;6);(6;5);(-5;-6);(-6;-5)}

=>(x;2y)∈{(1;29);(30;0);(-1;-31);(-30;-2);(2;14);(15;1);(-2;-16);(-15;-3);(3;9);(10;2);(-3;-11);(-10;-4);(5;5);(6;4);(-5;-7);(-6;-6)}

=>(x;y)∈{(1;29/2);(30;0);(-1;-31/2);(-30;-1);(2;7);(15;1/2);(-2;-8);(-15;-3/2);(3;9/2);(10;1);(-3;-11/2);(-10;-2);(5;5/2);(6;2);(-5;-7/2);(-6;-3)}

b: \(\frac{4}{x}+\frac{y}{3}=\frac56\)

=>\(\frac{4}{x}=\frac56-\frac{y}{3}=\frac{5-2y}{6}\)

=>x(5-2y)=24

=>x(2y-5)=-24

=>(x;2y-5)∈{(1;-24);(-24;1);(-1;24);(24;-1);(2;-12);(-12;2);(-2;12);(12;-2);(3;-8);(-8;3);(-3;8);(8;-3);(4;-6);(-6;4);(-4;6);(6;-4)}

=>(x;2y)∈{(1;-19);(-24;6);(-1;29);(24;4);(2;-7);(-12;7);(-2;17);(12;3);(3;-3);(-8;8);(-3;13);(8;2);(4;-1);(-6;9);(-4;11);(6;1)}

=>(x;y)∈{(1;-19/2);(-24;3);(-1;29/2);(24;2);(2;-7/2);(-12;7/2);(-2;17/2);(12;3/2);(3;-3/2);(-8;4);(-3;13/2);(8;1);(4;-1/2);(-6;9/2);(-4;11/2);(6;1/2)}

a: \(\frac{x}{3}-\frac{4}{y}=\frac15\)

=>\(\frac{x}{3}-\frac15=\frac{4}{y}\)

=>\(\frac{5x-3}{15}=\frac{4}{y}\)

=>y(5x-3)=60

=>(5x-3;y)∈{(1;60);(60;1);(-1;-60);(-60;-1);(2;30);(30;2);(-2;-30);(-30;-2);(3;20);(20;3);(-3;-20);(-20;-3);(4;15);(15;4);(-4;-15);(-15;-4);(5;12);(12;5);(-5;-12);(-12;-5);(6;10);(10;6);(-6;-10);(-10;-6)}

=>(5x;y)∈{(4;60);(63;1);(2;-60);(-57;-1);(5;30);(33;2);(1;-30);(-27;-2);(6;20);(23;3);(0;-20);(-17;-3);(7;15);(18;4);(-1;-15);(-12;-4);(8;12);(15;5);(-2;-12);(-9;-5);(9;10);(13;6);(-3;-10);(-7;-6)}

=>(x;y)∈{(4/5;60);(63/5;1);(2/5;-60);(-57/5;-1);(1;30);(33/5;2);(1/5;-30);(-27/5;-2);(6/5;20);(23/5;3);(0;-20);(-17/5;-3);(7/5;15);(18/5;4);(-1/5;-15);(-12/5;-4);(8/5;12);(3;5);(-2/5;-12);(-9/5;-5);(9/5;10);(13/5;6);(-3/5;-10);(-7/5;-6)}

1. Thu gọn biểu thức - Hoc24 làm rồi mà bạn?

1.

a) \(=x^2-6x+9+3x^2-15x=4x^2-21x+9\)

b) \(=9x^2+12x+4-x^2+9=8x^2+12x+13\)

2.

a) \(\Leftrightarrow x^2+8x+16-x^2+4-5=0\\ \Leftrightarrow8x=-15\\ \Leftrightarrow x=-\dfrac{15}{8}\)

b) \(\Leftrightarrow9x^2-6x+1-8x^2+12x-2x+3-5-x^2=0\\ \Leftrightarrow4x=1\\ \Leftrightarrow x=\dfrac{1}{4}\)

a \(\dfrac{2}{3}x+\dfrac{1}{3}=\dfrac{1}{5}\\ \dfrac{2}{3}x=\dfrac{1}{5}-\dfrac{1}{3}\\ \dfrac{2}{3}x=\dfrac{-2}{15}\\ x=-\dfrac{2}{15}:\dfrac{2}{3}\\ x=-\dfrac{1}{5}\)   b) \(\dfrac{4}{5}-\dfrac{5}{3}x=-2\\ \dfrac{5}{3}x=\dfrac{4}{5}+2\\ \dfrac{5}{3}x=\dfrac{14}{5}\\ x=\dfrac{14}{5}:\dfrac{5}{3}\\ x=\dfrac{42}{25}\)c) \(\dfrac{1}{5}+\dfrac{5}{3}:x=\dfrac{1}{2}\\ \dfrac{5}{3}:x=\dfrac{1}{2}-\dfrac{1}{5}\\ \dfrac{5}{3}:x=\dfrac{3}{10}\\ x=\dfrac{5}{3}:\dfrac{3}{10}\\ x=\dfrac{50}{9}\)d) \(\dfrac{5}{7}:x-3=-\dfrac{2}{7}\\ \dfrac{5}{7}:x=3-\dfrac{2}{7}\\ \dfrac{5}{7}:x=\dfrac{19}{7}\\ x=\dfrac{5}{7}:\dfrac{19}{7}\\ x=\dfrac{5}{19}\)

Mơn