Bài 5: Lũy thừa của một số hữu tỉ

Ta có :

\(8^7-2^{18}=\left(2^3\right)^7-2^{18}\)

\(=2^{21}-2^{18}\)

\(=2^{18}\left(2^3-1\right)\)

\(=2^{18}.7\)

\(=2^{17}.2.7\)

\(=2^{17}.14⋮14\)

Vậy \(8^7-2^{18}⋮14\rightarrowđpcm\)

Ta có:

\(8^7-2^{18}=\left(2^3\right)^7-2^{18}\)

\(=2^{21}-2^{18}=2^{18}.\left(2^3-1\right)\)

\(=2^{17}.2.7=2^{17}.14\)

Vì \(14⋮14\) nên \(2^{17}.14⋮14\)

=> \(8^7-2^{18}⋮14\) (đpcm)

Chúc bạn học tốt!!!

Giải:

\(8^7-2^{18}\)

\(=\left(2^3\right)^7-2^{18}\)

\(=2^{21}-2^{18}\)

\(=2^{18}.\left(2^3-1\right)\)

\(=2^{18}.\left(8-1\right)\)

\(=2^{18}.7\)

\(=2^{17}.2.7\)

\(=2^{17}.14⋮14\) (đpcm)

Chúc bạn học tốt!

Ta có :

\(x+y+z=18\)

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+y+z}{2+3+4}=\dfrac{18}{9}=2\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{2}=2\Leftrightarrow x=4\\\dfrac{y}{3}=2\Leftrightarrow y=6\\\dfrac{z}{4}=2\Leftrightarrow z=8\end{matrix}\right.\)

Vậy ...

Ta có :

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+y+z}{2+3+4}=\dfrac{18}{9}=2\)

\(\dfrac{x}{2}=2\Rightarrow x=4\)

\(\dfrac{y}{3}=2\Rightarrow y=6\)

\(\dfrac{z}{4}=2\Rightarrow z=8\)

Theo bài ra, ta có: z+y+z=18

và \(\dfrac{x}{2}\)= \(\dfrac{y}{3}\)=\(\dfrac{z}{4}\)

=> =\(\dfrac{x}{2}\) =\(\dfrac{y}{3}\) =\(\dfrac{z}{4}\) =\(\dfrac{x+y+z}{2+3+4}\) =\(\dfrac{18}{9}\) =2

-> \(\dfrac{x}{2}\)=2 => x= 2.2=4

-> \(\dfrac{y}{3}\) =2 => x= 3.2=6

-> \(\dfrac{z}{4}\)=2 => x= 4.2=8

Vậy x=4; y=6; z=8

chúc bạn học tốt

\(=\dfrac{5^{32}\cdot5^{43}\cdot2^{86}}{\left(-2\right)^{87}\cdot5^{75}}=\dfrac{1}{-2}=-\dfrac{1}{2}\)

Đặt \(\dfrac{x}{5}\) = \(\dfrac{y}{4}\) = k

Do đó: x = 5k, y = 4k

Ta có: x² - y² = 36

\(\Rightarrow\) (5k)² - (4k)² = 36

25k² - 16k² = 36

9k² = 36

k² = 4

\(\Rightarrow\) k = 2

Vậy x = 5k = 5.2 = 10

y = 4k = 4.2 = 8

~ Yorin ~

\(\frac{4^{20}(2^{20}+1)}{4^{15}(4^{10}+1)}=4^5=1024 \)

Bài 2

Ta có; \((x-2)^{2012}\ge0\)

\(|y^2-9|^{2014}\ge0\)

=>\((x-2)^{2012}+|y^2+9|^{2014}\ge0\)

Mà \((x-2)^{2012}+|y^2+9|^{2014}=0\)

=>x-2=0=>x=2

y^2-9=0=>y=+-3

Tham khảo

2A=2^101-2^100+2^99-2^98+...+2^3+2^2

2A-A=2^101-2^100+2^99-2^98+...+2^3+2^2-2^100+2^99-2^98+2^97+...+2^2-2

A=2^100-2

Ta có :

(0,36)⁸=(0,6.0,6)⁸=(0,6²)⁸=0,6^2.8=0,6¹⁶

(0,216)⁴=(0,6.0,6.0,6)⁴=(0,6³)⁴=0,6^3.4=0,6¹²

Ta có:

\(\left(0,36\right)^8=\left(0,6.0,6\right)^8=\left(0,6^2\right)^8=0,6^{16}\)

\(\left(0,216\right)^4=\left(0,6.0,6.0,6\right)^4=\left(0,6^3\right)^4=0,6^{12}\)

Ta có : -3/4=x/5

➜\(\dfrac{-3}{x}\) = \(\dfrac{4}{5}\)

➜-3.5 = x.4

➞-15 =x.4

➜x = \(\dfrac{-15}{4}\)

Theo bài ra ta có :

\(\dfrac{-3}{4}=\dfrac{x}{5}\Rightarrow\left(-3\right)\cdot5=4\cdot x\)

\(\Rightarrow-15=4x\)

\(\Rightarrow4x=-15\)

\(\Rightarrow x=\left(-15\right):4=-\dfrac{15}{4}\)

Vậy x = \(\dfrac{-15}{4}\)

Giải:

\(\dfrac{-3}{4}=\dfrac{x}{5}\Rightarrow x=-\dfrac{3.5}{4}=-\dfrac{15}{4}.\)

Vậy.....

Ta có : S = 2² + 4² + 6² + ... + 20² = 1540

Suy ra S = ( 1 . 2 )² + ( 2 . 2 )² + ( 3 . 2 )² + ... + ( 10 . 2 )² = 1540

Suy ra S = 1² . 2² + 2² . 2² + 3² . 2² + ... + 10² . 2² = 1540

Suy ra S = ( 1² + 2² + 3² + ... + 10² ) . 2² = 1540

Suy ra S = M . 4 = 1540

Suy ra M = 1540 : 4

Suy ra M = 385

Vậy M = 385

Ta có : S = 2² + 4² + 6² + ... + 20² = 1540

nên S = ( 1 . 2 )² + ( 2 . 2 )² + ( 3 . 2 )² + ... + ( 10 . 2 )² = 1540

          = 1² . 2² + 2² . 2² + 3² . 2² + ... + 10² . 2² = 1540

          = ( 1² + 2² + 3² + ... + 10² ) . 2² = 1540

 →S = M . 4 = 1540

→ M = 1540 : 4 = 385

có sai đề ko 6 → 9 ấy