\(\left(2x+3\right)^{1998}+\left(3y-5\right)^{2000}\le0\)
\(\left\{{}\begin{matrix}\left(2x+3\right)^{1998}\ge0\\\left(3y-5\right)^{2000}\ge0\end{matrix}\right.\)
\(\Rightarrow\left(2x+3\right)^{1998}+\left(3y-5\right)^{2000}\ge0\)
\(\Rightarrow\left[{}\begin{matrix}\left(2x+3\right)^{1998}+\left(3y-5\right)^{2000}\ge0\\\left(2x+3\right)^{1998}+\left(3y-5\right)^{2000}\le0\end{matrix}\right.\)
\(\Rightarrow\left(2x+3\right)^{1998}+\left(3y-5\right)^{2000}=0\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left(2x+3\right)^{1998}=0\Rightarrow2x+3=0\Rightarrow2x=-3\Rightarrow x=-\dfrac{3}{2}\\\left(3y-5\right)^{2000}=0\Rightarrow3y-5=0\Rightarrow3y=5\Rightarrow y=\dfrac{5}{3}\end{matrix}\right.\)
2)
\(\left(-16\right)^{11}=-\left[\left(2^4\right)^{11}\right]=-\left(2^{44}\right)\)
\(\left(-32\right)^9=-\left[\left(2^5\right)^9\right]=-\left(2^{45}\right)\)
\(-\left(2^{44}\right)>-\left(2^{45}\right)\Rightarrow\left(-16\right)^{11}>\left(-32\right)^9\)
\(\left(2^2\right)^3=2^8\)
\(2^{2^3}=2^8\)
\(2^8=2^8\Rightarrow\left(2^2\right)^3=2^{2^3}\)
\(2^{3^2}=2^9\)
\(2^{2^3}=2^8\)
\(2^9>2^8\Rightarrow2^{3^2}>2^{2^3}\)
