\(\Rightarrow16-3x=504:72=7\\ \Rightarrow3x=16-7=9\Rightarrow x=3\\ \left(2^2\cdot x-5^2\right)\cdot3^8=3^9\\ \Rightarrow4x-25=3^9:3^8=3\\ \Rightarrow4x=28\Rightarrow x=7\)

504 : (16 - 3x) = 72 (ĐK: \(x\ne\dfrac{16}{3}\))

<=> 16 - 3x = 504 : 72

<=> 16 - 3x = 7

<=> 16 - 7 = 3x

<=> 3x = 9

<=> x = 3 (tM)

(2²x - 5²) . 3⁸ = 3⁹

<=> (4x - 25) . 6561 = 19683

<=> 4x - 25 = 19683 : 6561

<=> 4x - 25 = 3

<=> 4x = 3 + 25

<=> 4x = 28

<=> x = 7 

Bài 2:

a. $=58(75+50-25)=58.100=5800$
b. $=27.8+4.9-5=216+36-5=247$

Bài 3:

a. 

$(x-38):16=12$

$x-38=16\times 12=192$
$x=192+38 = 230$
b.

$10+2x=4^5:4^3=4^2=16$

$2x=16-10=6$

$x=6:2=3$
c.

$440+2(125-x)=546$

$2(125-x)=546-440=106$

$125-x=106:2=53$

$x=125-53=72$

d.

$(x-15):5+20=22$
$(x-15):5=22-20=2$

$x-15=2\times 5=10$

$x=10+15=25$

e.

$2x-138=2^3.3^2=8.9=72$

$2x=72+138 = 210$

$x=210:2=105$

Bài 3:

f.

$2.3^x-5=7^2$

$2.3^x=7^2+5=54$
$3^x=54:2=27=3^3$

$\Rightarrow x=3$

g.

$7x-3^3=2^7:2^4$

$7x-27=2^3=8$

$7x=27+8=35$

$x=35:7=5$
h.

$427-(x+100)=227$

$x+100=427-227 = 200$

$x=200-100=100$

i.

$2x-138=2^3.3^2=8.9=72$
$2x=72+138 = 210$

$x=210:2=105$

k.

$(6x-18):3+25.2=78$

$(2x-6)+50=78$

$2x-6=78-50=28$

$2x=28+6=34$

$x=34:2=17$

a.

$S=1+2+2^2+2^3+...+2^{2017}$
$2S=2+2^2+2^3+2^4+...+2^{2018}$

$\Rightarrow 2S-S=(2+2^2+2^3+2^4+...+2^{2018}) - (1+2+2^2+2^3+...+2^{2017})$

$\Rightarrow S=2^{2018}-1$

b.

$S=3+3^2+3^3+...+3^{2017}$
$3S=3^2+3^3+3^4+...+3^{2018}$

$\Rightarrow 3S-S=(3^2+3^3+3^4+...+3^{2018})-(3+3^2+3^3+...+3^{2017})$

$\Rightarrow 2S=3^{2018}-3$
$\Rightarrow S=\frac{3^{2018}-3}{2}$
 

Câu c, d bạn làm tương tự a,b. 

c. Nhân S với 4. Kết quả: $S=\frac{4^{2018}-4}{3}$

d. Nhân S với 5. Kết quả: $S=\frac{5^{2018}-5}{4}$

a, 36:{336:[200–(12+8.20)]}

= 36:{336:[200–(12+160)]}

= 36:{336:[200–172]}

= 36:{336:28}

= 36:12 = 3

b, {145–[130–(246–236)]:2}.5

= {145–[130–10:2]}.5

= {145–130}.5

= 20.5 = 100

c, 100:{250:[450–(4. 5 3 – 2 2 .25]}

= 100:{250:[450–400]}

= 100:{250:50}

= 100:5 = 20

d, 798+100:[16–2.( 5 2 –22)]

= 798+100:10

= 798+10 = 808

e, (6954+1525:5+47.19).(29–58.2)

= (6954+1525:5+47.19).0 = 0

f,  2 4 .157– 2 4 .58+16

= 16.(157–58+1) = 1600

\(a)\) \(5^{13}:5^{10}-25.2^2=5^3-25.4=125-100=25\)

\(b)\) \(20:2^2+5^9:5^8=20:4+5^1=5+5=10\)

\(c)\) \(100:5^2+7.3^2=100:25+7.9=4+36=40\)

\(d)\) \(84:4+3^9:3^7+5^0=84:4+3^2+1=21+9+1=31\)

\(e)\)

\(29-\left[16+3.\left(51-49\right)\right]=29-\left[16+3.2\right]=29-\left[16+6\right]=29-22=7\)

\(f)\) \(5.2^2+98:7^2=5.4+98:49=20+2=22\)

\(g)\) \(3^{11}:3^9-147:7^2=3^2-147:49=9-3=6\)

\(295-\left(31-2^2.5\right)^2=295-\left(31-4.5\right)^2=295-\left(31-20\right)^2=295-11^2=295-121=174\)

\(7^{18}:7^{16}+2^2.3^2=7^2+4.9=49+36=85\)

a: \(5^{13}:5^{10}-25\cdot2^2\)

\(=5^3-25\cdot4\)

=125-100

=25

b: \(20:2^2+5^9:5^8\)

\(=20:4+5\)

=5+5

=10

a: \(12+2^2+3^2+4^2+5^2\)

\(=12+4+9+16+25\)

\(=16+50=66\)

\(\left(1+2+3+4+5\right)^2=15^2=225\)

=>\(12+2^2+3^2+4^2+5^2< \left(1+2+3+4+5\right)^2\)

b: \(1^3+2^3+3^3+4^3=\left(1+2+3+4\right)^2< \left(1+2+3+4\right)^3\)

c: \(5^{202}=5^2\cdot5^{200}=25\cdot5^{200}>16\cdot5^{200}\)

d: \(18\cdot4^{500}=18\cdot2^{1000}\)

\(2^{1004}=2^4\cdot2^{1000}=16\cdot2^{1000}\)

=>\(18\cdot4^{500}>2^{1004}\)

e: \(2022\cdot2023^{2024}+2023^{2024}=2023^{2024}\left(2022+1\right)\)

\(=2023^{2025}\)