Bài 1:

2^\(x\) = 4

2\(^x\) = 2²

 \(x=2\)

Vậy \(x=2\)

Bài 2:

2\(^x\) = 8

2\(^x\) = 2³

\(x=3\)

Vậy \(x=3\)

a) \(\dfrac{10^{12}+5^{11}.2^9-5^{13}.2^8}{4.5^5.10^6}\)

\(=\dfrac{2^{12}.5^{12}+5^{11}.2^9-5^{13}.2^8}{2^2.5^5.2^6.5^6}\)

\(=\dfrac{2^{12}.5^{12}+5^{11}.2^9-5^{13}.2^8}{2^8.5^{11}}\)

\(=\dfrac{\left(2^8.5^{11}\right)\left(2^4.5+2-5^2\right)}{2^8.5^{11}}\)

\(=2^4.5+2-5^2\)

\(=57\)

b) \(\dfrac{\left[5\left(x-y\right)^4-3\left(x-y\right)^3+4\left(x-y\right)^2\right]}{\left(y-x\right)^2}\)

\(=\dfrac{\left(x-y\right)^2\left[5\left(x-y\right)^2-3\left(x-y\right)+4\right]}{\left(y-x\right)^2}\)

\(=\dfrac{\left(x^2+y^2-2xy\right)\left[5\left(x-y\right)^2-3\left(x-y\right)+4\right]}{\left(y^2+x^2-2xy\right)}\)

\(=5\left(x-y\right)^2-3\left(x-y\right)+4\)

c) \(\dfrac{\left(x+y\right)^5-2\left(x+y\right)^4+3\left(x+y\right)^3}{-5\left(x+y\right)^3}\)

\(=\dfrac{\left(x+y\right)^3\left[5\left(x+y\right)^2-2\left(x+y\right)+3\right]}{-5\left(x+y\right)^3}\)

\(=\dfrac{5\left(x+y\right)^2-2\left(x+y\right)+3}{-5}\)

7: \(\left(xy+4\right)^2-\left(2x+2y\right)^2\)

=(xy+4-2x-2y)(xy+4+2x+2y)

=[x(y-2)-2(y-2)][x(y+2)+2(y+2)]

=(x-2)(y-2)(x+2)(y+2)

8: \(81x^2-64y^2=\left(9x\right)^2-\left(8y\right)^2\)

=(9x-8y)(9x+8y)

9: \(\left(a^2+b^2+5\right)^2-4\left(ab+2\right)^2\)

\(=\left(a^2+b^2+5\right)^2-\left(2ab+4\right)^2\)

\(=\left(a^2+b^2+5-2ab-4\right)\left(a^2+b^2+5+2ab+4\right)\)

\(=\left\lbrack\left(a-b\right)^2+1\right\rbrack\left\lbrack\left(a+b\right)^2+9\right\rbrack\)

10: \(\left(x-1\right)^2-\left(x+1\right)^2\)

=(x-1-x-1)(x-1+x+1)

=2x*(-2)=-4x

11: \(8x^3-\frac18=\left(2x\right)^3-\left(\frac12\right)^3=\left(2x-\frac12\right)\left(4x^2+2x\cdot\frac12+\frac14\right)\)

\(=\left(2x-\frac12\right)\left(4x^2+x+\frac14\right)\)

12: \(\frac{1}{25}x^2-64y^2=\left(\frac15x\right)^2-\left(8y\right)^2=\left(\frac15x-8y\right)\left(\frac15x+8y\right)\)

13: \(x^3+\frac{1}{27}=x^3+\left(\frac13\right)^3=\left(x+\frac13\right)\left(x^2-\frac13x+\frac19\right)\)

a) 89-(73-x)=20

=>73-x=89-20

=>73-x=69

=>x=73-69

=>x=4

A . 89 - ( 73 - x ) = 20

              73 - x   = 89 - 20

              73 - x   = 69

              \(\Rightarrow\)x = 4

B .

câu a:

3\(^2\) x 5 + 2\(^3\) x 10 - 81 : 3

= 9 x 5 + 8 x 10 - 27

= 45 + 80 - 27

= 125 - 27

= 98

Câu c:

100 : 5\(^2\) + 7 x 3\(^2\)

= 100 : 25 + 7 x 9

= 4 + 63

= 67

Bài 9,

6²x73+36x3³=36x73+36x27=36(73+27)=36x100=3600.

197-\([\)6x(5-1)²+2022⁰\(]\):5=197-\([\)6x16+1\(]\):5=197-97:5=197-97/5=888/5.

Bài 10,

21-4x=13

=>4x=21-13=8

=>x=8:4=2.

30:(x-3)+1=4⁵:4³=4²=16

=>30:(x-3)=16-1=15

=>x-3=30:15=2

=>x=2+3=5.

(x-1)³+5x6=38

=>(x-1)³+30=38

=>(x-1)³=38-30=8=2³

=>x-1=2

=>x=3.

a, (-0,2)² \(\times\) 5 - \(\dfrac{2^{13}\times27^3}{4^6\times9^5}\)

= 0,04 \(\times\) 5 - \(\dfrac{2^{13}\times3^9}{2^{12}\times3^{10}}\)

= 0,2 - \(\dfrac{2}{3}\)

= \(\dfrac{2}{10}\) - \(\dfrac{2}{3}\)

=  - \(\dfrac{7}{15}\)

b, \(\dfrac{5^6+2^2.25^3+2^3.125^2}{26.5^6}\)

 = \(\dfrac{5^6+4.5^6+8.5^6}{26.5^6}\)

= \(\dfrac{5^6.\left(1+4+8\right)}{26.5^6}\)

= \(\dfrac{1}{2}\)

a, (-0,2)2 $\times$ 5 - 213×27346×9546×95213×273​

= 0,04 $\times$ 5 - 213×39212×310212×310213×39​

= 0,2 - 2332​

= 210102​ - 2332​

=  - 715157​

b, 56+22.253+23.125226.5626.5656+22.253+23