n=2

\(\Rightarrow2^{3n-n}=16=2^4\Rightarrow2n=4\Rightarrow n=2\)

\(\dfrac{8^5\cdot\left(-5\right)^8+\left(-2\right)^5\cdot10^9}{2^{16}\cdot5^7+20^8}\)

\(=\dfrac{2^{15}\cdot5^8-2^{14}\cdot5^9}{2^{16}\cdot5^7+2^{16}\cdot5^8}\)

\(=\dfrac{2^{14}\cdot5^8\left(2-5\right)}{2^{16}\cdot5^7\cdot\left(1+5\right)}\)

\(=\dfrac{5\cdot\left(-3\right)}{4\cdot6}=\dfrac{-15}{24}=\dfrac{-5}{8}\)

a, 16/2n=2

<=>2n=8

<=>n=4

b, (-3)^n =-27*81=-2187

n=7( vì (-3)^7 =-2187

c, 8^n : 2^n =4

<=> (8:2)^n=4

4^n=4

n=1

a: f(1)=1

=>\(a\cdot1^2+b\cdot1+1=1\)

=>a+b=0

f(-1)=3

=>\(a\cdot\left(-1\right)^2+b\cdot\left(-1\right)+1=3\)

=>a-b=2

mà a+b=0

nên \(a=\dfrac{2+0}{2}=1;b=2-1=1\)

b: a=1 và b=1 nên \(f\left(x\right)=x^2+x+1\)

\(\Leftrightarrow\dfrac{n}{f\left(n\right)}=\dfrac{n}{n^2+n+1}\)

Gọi d=ƯCLN(n^2+n+1;n)

=>\(\left\{{}\begin{matrix}n^2+n+1⋮d\\n⋮d\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}n^2+n+1⋮d\\n\left(n+1\right)⋮d\end{matrix}\right.\)

=>\(\left(n^2+n+1\right)-n\left(n+1\right)⋮d\)

=>\(1⋮d\)

=>d=1

=>ƯCLN(n^2+n+1;n)=1

=>\(\dfrac{n}{f\left(n\right)}=\dfrac{n}{n^2+n+1}\) là phân số tối giản

ai chơi minecraft hay blockman go thì hãy sud kênh

UCiBjk1S06KCJabPK9vG2q1w

Ta có: \(\left(3x^2-51\right)^{2n}=\left(-24\right)^{2n}\)

\(\Leftrightarrow\orbr{\begin{cases}3x^2-51=-24\\3x^2-51=24\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x^2=27\\3x^2=75\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x^2=9\\x^2=25\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\pm3\\x=\pm5\end{cases}}\)

Vậy \(x\in\left\{\pm3;\pm5\right\}\)

a) \(5^6:5^5+\left(\dfrac{4}{9}\right)^0=5^{6-5}+1=5+1=6\)

b) \(\left(\dfrac{3}{7}\right)^{21}:\left(1-\dfrac{40}{49}\right)^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left[\left(\dfrac{3}{7}\right)^2\right]^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^6\)

\(=\left(\dfrac{3}{7}\right)^{21-6}=\left(\dfrac{3}{7}\right)^{15}\)

c) \(\left(\dfrac{2}{3}\right)^3-\left(\dfrac{-52}{3}\right)^0+\dfrac{4}{9}\)

\(=\dfrac{8}{27}-1+\dfrac{4}{9}\)

\(=\dfrac{8-27+12}{27}=-\dfrac{7}{27}\)

\(a)5^6:5^5+\left(\dfrac{4}{9}\right)^0=5^1+1=6\)

\(b,\left(\dfrac{3}{7}\right)^{21}:\left(1-\dfrac{40}{49}\right)^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{49-40}{49}\right)^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{9}{49}\right)^3=\left(\dfrac{3}{7}\right)^{21}:[\left(\dfrac{3}{7}\right)^2]^3\)

\(=\left(\dfrac{3}{7}\right)^{21}:\left(\dfrac{3}{7}\right)^6=\left(\dfrac{3}{7}\right)^{21-6}\)

\(=\left(\dfrac{3}{7}\right)^{15}\)

\(c,3.\left(\dfrac{2}{3}\right)^3-\left(\dfrac{-52}{3}\right)^0+\dfrac{4}{9}\)

\(=3.\dfrac{8}{27}-1+\dfrac{4}{9}\)

\(=\dfrac{8}{9}-1+\dfrac{4}{9}\)

\(=\dfrac{8-9+4}{9}=\dfrac{1}{3}\)

Ta có: \(\frac{2000}{-2001}=-\frac{2000}{2001}=-\left(\frac{2001-1}{2001}\right)=-\left(\frac{2001}{2001}-\frac{1}{2001}\right)=-\left(1-\frac{1}{2001}\right)=-1+\frac{1}{2001}\)

       \(-\frac{2003}{2002}=-\left(\frac{2002+1}{2002}\right)=-\left(\frac{2002}{2002}+\frac{1}{2002}\right)=-\left(1+\frac{1}{2002}\right)=-1-\frac{1}{2002}\)

Vì \(\frac{1}{2001}>-\frac{1}{2002}\) nên \(-1+\frac{1}{2001}>-1-\frac{1}{2002}\)

hay \(\frac{2000}{-2001}>-\frac{2003}{2002}\)