\(\left[\left(-\dfrac{1}{5}\right)^n\right]^2=\dfrac{1}{625}\) \(\Leftrightarrow\left(-\dfrac{1}{5}\right)^n=\pm\sqrt{\dfrac{1}{625}}=\pm\dfrac{1}{25}\)
\(th1:\left(-\dfrac{1}{5}\right)^n=\dfrac{1}{25}=\left(-\dfrac{1}{5}\right)^2\Rightarrow n=2\)
\(th2:\left(-\dfrac{1}{5}\right)^n=\dfrac{-1}{25}\) (không có giá trị nào của n thỏa mãn)
vậy \(n=2\)
\(\left[\left(-\dfrac{1}{5}\right)^n\right]^2=\dfrac{1}{625}\)
\(\Rightarrow\left(\dfrac{1}{5}\right)^{2n}=\left(\dfrac{1}{5}\right)^4\)
Vì \(\dfrac{1}{5}\ne-1;\dfrac{1}{5}\ne0;\dfrac{1}{5}\ne1\) nên \(2n=4\Rightarrow n=2\)
Vậy.............
Chúc bạn học tốt!!!
