\(3A=3+3^2+...3^{2003}\)

\(3A-A=\left(3-3\right)+\left(3^2-3^2\right)+...+3^{2003}-1\)

\(\Leftrightarrow\Leftrightarrow A=\frac{3^{2003}-1}{2}\)

bao giờ vào nhà tao tao chỉ cho

a: A=3^2(1^2+2^2+...+10^2)

=9*385

=3465

b: B=2^3(1^3+2^3+...+10^3)

=8*3025

=24200

7/6

1/5

Tính: 2/3 + 1/2 = …7/6.

Tính: 1/2 × 2/3 × 3/4 × 4/5 = 24/120 = 1/5

7/6

1/5

1.

2^3 . 4^4 . 16^2

= 2^3 . 2^8 . 2^8

= 2^19

2. 

8^6 : 2^3

= 2^18 : 2^3

= 2^15

Mấy câu kia tương tự thôi :D

1) 2³.4⁶.16²=2³.(2²)⁶.(2⁴)²=2³.2¹².2⁸= 2²³

2) 8⁶ : 2³ = (2³)⁶ : 2³ = 2¹⁸ : 2³ = 2¹⁵

3) 27³:3³ =(3³)³ : 3³ = 3⁹ : 3³ = 3⁶

4) 15³ : 5³ = (3.5)³ : 5³ = 3³

\(2^3.4^6.16^2=2^3.2^{12}.2^8=2^{3+12+8}=2^{23}\)

\(8^6:2^3=2^{18}:2^3=2^{18-3}=2^{15}\)

\(27^3:3^3=3^9:3^3=3^6\)

\(15^3:5^3=3.5^3:5^3=3.\left(5^3:5^3\right)=3:1=3\)

thích làm mỗi bài 3 vi các bai khac vua de, vua dai viet mệt

3) 3ⁿ : 3^n-1 = 3^n-n+1 = 3

Số nguyên n thỏa mãn đẳng thức -81/(-3)^n =-243 <=> (-3)^n x (-243) = -81 <=> (-3)^n x (-3)^5 = (-3)^4 

<=> (-3)^n = (-3)^4 : (-3)^5 <=> (-3)^n = (-3)^4-5  <=> (-3)^n = (-3)^(-1) => n=-1. 

ta có: a + b=-2 ; a^2 + b^2 = 52

=> (a+b)^2 = 4 => a^2 + 2ab + b^2 = 4

=> 52 + 2ab= 4

=> 48= -2ab

=> ab= -24

a^3 + b^3 = (a+b)( a^2-ab+ b^2)

=> a^3 + b^3 = -2.(52+24)= -2. 76= -152

Bài 1:

a, 3\(\dfrac{2}{5}\) - \(\dfrac{1}{2}\) 

= \(\dfrac{17}{5}\) - \(\dfrac{1}{2}\) 

= \(\dfrac{34}{10}\) - \(\dfrac{5}{10}\)

= \(\dfrac{29}{10}\)

b, \(\dfrac{4}{5}\) + \(\dfrac{1}{5}\) x \(\dfrac{3}{4}\)

= \(\dfrac{4\times4}{5\times4}\) + \(\dfrac{1\times3}{5\times4}\)

= \(\dfrac{16}{20}\) + \(\dfrac{3}{20}\)

= \(\dfrac{19}{20}\)

c, 4\(\dfrac{4}{9}\) : 2\(\dfrac{2}{3}\) + 3\(\dfrac{1}{6}\)

= \(\dfrac{40}{9}\) : \(\dfrac{8}{3}\) + \(\dfrac{19}{6}\)

= \(\dfrac{5}{3}\) + \(\dfrac{19}{6}\)

= \(\dfrac{10}{6}\) + \(\dfrac{19}{6}\)

= \(\dfrac{29}{6}\)

Bài 2:

   3\(\dfrac{2}{5}\) + 2\(\dfrac{1}{5}\) 

= \(\dfrac{17}{5}\) + \(\dfrac{11}{5}\)

= \(\dfrac{28}{5}\)

b, 7\(\dfrac{1}{6}\) : 5\(\dfrac{2}{3}\)

= \(\dfrac{43}{6}\) : \(\dfrac{17}{3}\)

= \(\dfrac{43}{34}\)

Bài 3:

a, 800 kg 5g > 8,005 kg

b, 9 ha 4 dam² < 9\(\dfrac{5}{100}\) ha

c, 5m 5mm > 5,0005 m

d, 250 kg > \(\dfrac{1}{5}\) tấn

a: \(x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)\)

\(=3^3-3\cdot3\cdot\left(-2\right)\)

\(=27+18=45\)

b: \(\left(x^3+y^3\right)^2=45^2=2025\)