Bài 6: Lũy thừa của một số hữu tỉ (tiếp theo...)

a,

 \(\left(5x+3\right)^2=\dfrac{25}{9}\\ \Rightarrow\left[{}\begin{matrix}5x+3=\dfrac{5}{3}\\5x+3=-\dfrac{5}{3}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{4}{15}\\x=-\dfrac{7}{6}\end{matrix}\right.\)

b,

\(\left(-\dfrac{1}{2}x+3\right)^3=-\dfrac{1}{125}\\ \Rightarrow-\dfrac{1}{2}x+3=-\dfrac{1}{5}\\ \Rightarrow x=\dfrac{32}{5}\)

c,

a, \(2^3.2^5=2^8=256\)   

    \(\left(-3\right)^9:\left(-3\right)^5=\left(-3\right)^4=81\)     

    \(\left(-6\right)^9.6^5=\left(-1\right)^9.6^9.6^5=\left(-1\right).6^{14}\\ \left(\dfrac{1}{2}\right)^5=\dfrac{1}{32}\)

b, \(\left(\dfrac{3}{5}\right)^6.\left(\dfrac{5}{3}\right)^6=\left(\dfrac{3}{5}. \dfrac{5}{3}\right)^6=1^6=1\\ \left(-\dfrac{7}{8}\right)^9:\left(\dfrac{7}{4}\right)^9=\left(-\dfrac{7}{8}:\dfrac{7}{4}\right)^9=\left(-\dfrac{1}{2}\right)^9=-\dfrac{1}{512}\\ \left(\left(-\dfrac{1}{2}\right)^2\right)^3=\left(\dfrac{1}{2}\right)^{...}\Rightarrow\left(\dfrac{1}{64}\right)=\left(\dfrac{1}{2}\right)...\Rightarrow\left(\dfrac{1}{64}\right)=\left(\dfrac{1}{2}\right)^6\)

c, \(\left(\dfrac{2}{3}\right)^8=\left(\left(\dfrac{2}{3}\right)^4\right)^{...}\Rightarrow\left(\left(\dfrac{2}{3}\right)^4\right)^2=\left(\left(\dfrac{2}{3}\right)^4\right)^{...}\Rightarrow\left(\dfrac{2}{3}\right)^8=\left(\left(\dfrac{2}{3}\right)^4\right)^2\\ \left(\dfrac{1}{3}\right)^{12}:\left(-\dfrac{3}{9}\right)^{12}=\left(\dfrac{1}{3}.\left(-3\right)\right)^{12}=\left(-1\right)^{12}=1\\ \left(\dfrac{1}{3}\right)^{12}:\left(\dfrac{1}{3}\right)^{10}=\left(\dfrac{1}{3}\right)^2=\dfrac{1}{9}\)

???  Sao tui chẳng thấy j nhể

\(125^4:\left(\dfrac{25}{4}\right)^6=5^{12}:\dfrac{5^{12}}{4^6}=4^6=4096\)

a) \(16^5+2^{15}=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{14}\cdot2\cdot33⋮66\)

b) \(3^{m+2}-2^{n+4}+3^m+2^n\)

\(=3^m\cdot9+3-2^n\left(2^4-1\right)\)

\(=3^m\cdot10-2^{n-1}\cdot30\)

\(=30\left(3^{m-1}-2^{n-1}\right)⋮30\)

a) \(A=16^5+2^{15}=2^{20}+2^{15}=2^{15}\left(2^5+1\right)=2^{15}\cdot33=2^{14}\cdot66⋮66\)

b) Sửa đề 

\(B=3^{n+2}-2^{n+4}+3^n+2^n=3^n\left(3^2+1\right)-2^n\left(2^4-1\right)=3^n\cdot10-2^n\cdot15\\ =3^{n-1}\cdot30-2^{n-1}\cdot30=30\left(3^{n-1}-2^{n-1}\right)⋮30\)

(với mọi n nguyên dương)

2^x +2^x+3=320

<=>2^x.(1+2³)=320

Ủa số lẻ rứa??

Ta có: \(2^x+2^{x+3}=320\)

\(\Leftrightarrow2^x\cdot9=320\)

\(\Leftrightarrow2^x=\dfrac{320}{9}\)

Đề sai rồi bạn

tham khảo tại: 

https://olm.vn/hoi-dap/detail/107805793416.html

Ta có :

2009²⁰⁰⁹ = (2009²)¹⁰⁰⁴ . 2009 = (.....1)¹⁰⁰⁴ . 2009 = (....1) . 2009 = ......9

Vậy 2009²⁰⁰⁹ tận cùng là chữ số 9.

Ta có: \(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

\(=2^{99}\left(2-1\right)+2^{97}\left(2-1\right)+...+2\left(2-1\right)\)

\(=2^{99}+2^{97}+...+2^3+2\)

\(\Leftrightarrow4A=2^{101}+2^{99}+...+2^5+2^3\)

\(\Leftrightarrow3A=2^{101}-2\)

\(\Leftrightarrow A=\dfrac{2^{101}-2}{3}\)

Ví dụ mình ghi 1 số có lũy thừa là \(10^9\)

Các bước làm: trong hình

\(A=\dfrac{n+2}{2n+4}=\dfrac{n+2}{2\cdot\left(n+2\right)}=\dfrac{1}{2}\)

\(B=\dfrac{2\dfrac{1}{2}}{5}=\dfrac{1}{2}\)

\(A=B\)

\(A=\dfrac{n+2}{2n+4}=\dfrac{n+2}{2\left(n+2\right)}=\dfrac{1}{2}\)

\(B=\dfrac{2+\dfrac{1}{2}}{5}=\dfrac{\dfrac{5}{2}}{5}=\dfrac{1}{2}\)

\(\Rightarrow A=B\)