\(2^n.16-2^{n+1}=2^6-2^3\\ \Leftrightarrow2^n.2^4-2^n.2=2^6-2^3\\ \Leftrightarrow2^n\left(2^4-2\right)=2^6-2^3\\ \Leftrightarrow2^n=\dfrac{2^6-2^3}{2^4-2}\\ \Leftrightarrow2^n=\dfrac{2\left(2^5-2^2\right)}{2\left(2^3-1\right)}\\ \Leftrightarrow2^n=\dfrac{28}{6}\\ \Leftrightarrow2^n=4\\ \Leftrightarrow2^n=2^2\\ \Leftrightarrow n=2\)

\(2^n.16-2^{n+1}=2^6-2^3\\ \Leftrightarrow2^n.2^4-2^{n+1}=64-8\\ \Leftrightarrow2^{n+4}-2^{n+1}=56\\ \Leftrightarrow2^{n+1}.\left(2^3-1\right)=56\\ \Leftrightarrow2^{n+1}.7=56\\ \Leftrightarrow2^{n+1}=\dfrac{56}{7}=8=2^3\\ \Leftrightarrow n+1=3\\ \Leftrightarrow n=2\)

\(2^n\cdot16-2^{n+1}=2^6-2^3\\ 2^n\cdot16-2^n\cdot2= 2^3\cdot\left(8-1\right)\\ 2^n\cdot\left(16-2\right)=8\cdot7\\ 2^n\cdot14=8\cdot7\\ 2^n\cdot\left(14:7\right)=8\\ 2^n\cdot2=8\\ 2^{n+1}=2^3\\ =>n+1=3\\ n=3-1\\ n=2\)

Lời giải:
a.

$(x-15).27=0$

$x-15=0:27=0$

$x=15+0=15$

b.

$23(42-x)=0$

$42-x=0$

$x=42$

c.

$(9x+2).3=60$

$9x+2=60:3=20$

$9x=18$

$x=2$
d.

$71+(26-3x):5=75$

$(26-3x):5=75-71=4$

$26-3x=4.5=20$

$3x=26-20=6$

$x=6:2=3$

giúp tôi nhá

a) 5(x+7) - 10 = 2^3 . 5

 5(x+7 ) -10 = 8 . 5 = 40

5(x+7) = 40 + 10 = 50

x + 7 = 50 : 5 = 10

x = 10 - 7 = 3

b) 2^6 + ( 5 + x ) = 3^4

  64 +  ( 5 + x ) = 81

5 + x = 81 - 64 = 17

x = 17 - 5 = 12

12+12-23=1

26+36-11=47

10+37-26=21

19+42-10=51

12+12-23= 1
26+32-11= 47
10+37-26= 21
19+42-10= 51

12+12-23= 1

26+32-11=47

10+37-26=21

19+42-10=51

e. = 12 - 25 + 38 + 25 - 38 + 88  - 250 

    = ( -25 + 25) + (38 - 38) + ( 12 + 88) - 250

   = -150

f. = (-12).44 + 44.(-88)

 = 44 ( -12 -88 )

= 44 . 100

= 4400

g. = -48 + 54 -77 -24 + 48 + 77

= (-48 + 48) + (-77+77) + (54 -24)

= 30

h. = 11.(-42) + 11.(-26) + 42.11 + 42.26 -26.11 - 42.26

 = \([11.\left(-42\right)+11.42]+\left[11.\left(-26\right)-26.11\right]+[42.26-42.26]\)

= 11. (-52)

= - 572

\(e.-\left(-12+25-38\right)+\left(25-38+88\right)-250\\ =12-25+38+25-38+88-250\\ =\left(25-25\right)+\left(38-38\right)+\left(12+88\right)-250\\ =0+0+100-250=-150\)

\(f.\left(-12\right)\cdot\left(67-23\right)+44\cdot\left(-88\right)\\ =\left(-12\right)\cdot44+44\cdot\left(-88\right)\\ =44\cdot\left[-12+\left(-88\right)\right]\\ =44\cdot\left(-100\right)=-4400\)

\(g.\left(-48+54-77\right)-\left(24-48-77\right)\\ =-48+54-77-24+48+77\\ =\left(48-48\right)+\left(54-24\right)+\left(77-77\right)\\ =0+30+0=30\)

\(h.11\cdot\left(-42-26\right)+42\cdot\left(11+26\right)-26\cdot11-42\cdot26\\ =11\cdot\left(-68\right)+42\cdot37-26\cdot11-42\cdot26\\ =-748+1554-286-1092=-572\)

Đặt vế trái bằng A n

Dễ thấy với n = 1 hệ thức đúng.

Giả sử đã có 

Ta có:

A

A

= 42 * { 23 + 51 +26 }

= 42 *    100

=4200
 

1. = 13

2. = 346

3.= -69

4. = -2600

5. -2150

trên đầu bài là giấu phẩy hay giấu nhân thế

\(a,2^2=4,2^3=8,2^4=16,2^5=32,2^6=64,2^7=128,2^8=256,2^9=512,2^{10}=1024\)

\(b,3^2=9,3^3=27,3^4=81,3^5=243\)

\(c,4^2=16,4^3=64,4^4=256\)

\(d,5^2=25,5^3=125,5^4=625\)

a: \(2^2=4\)

\(2^3=8\)

\(2^4=16\)

\(2^5=32\)

\(2^6=64\)

\(2^7=128\)

\(2^8=256\)

\(2^9=512\)

\(2^{10}=1024\)

b: \(3^2=9\)

\(3^3=27\)

\(3^4=81\)

\(3^5=243\)

c: \(4^2=64\)

\(4^3=256\)

\(4^4=1024\)

d: \(5^2=25\)

\(5^3=125\)

\(5^4=625\)