Câu hỏi của Nguyen Hoang Trang Thu

Question

So sánh :

$\left(-\frac{1}{27}\right)^{53}và\left(-\frac{1}{243}\right)^{23}$

Nguyễn Hoàng Tiến · Accepted Answer

$-\frac{1}{27}=-\frac{1}{3^3}$ => $\left(-\frac{1}{27}\right)^{53}=\left(\left(-\frac{1}{3}\right)^3\right)^{53}=\left(-\frac{1}{3}\right)^{159}$

$-\frac{1}{243}=-\frac{1}{3^5}$ => $\left(-\frac{1}{243}\right)^{23}=\left(\left(-\frac{1}{3}\right)^5\right)^{23}=\left(-\frac{1}{3}\right)^{115}$

vẬY $\left(-\frac{1}{27}\right)^{53}< \left(-\frac{1}{243}\right)^{23}$

Câu trả lời:

$-\frac{1}{27}=-\frac{1}{3^3}$ => $\left(-\frac{1}{27}\right)^{53}=\left(\left(-\frac{1}{3}\right)^3\right)^{53}=\left(-\frac{1}{3}\right)^{159}$

$-\frac{1}{243}=-\frac{1}{3^5}$ => $\left(-\frac{1}{243}\right)^{23}=\left(\left(-\frac{1}{3}\right)^5\right)^{23}=\left(-\frac{1}{3}\right)^{115}$

vẬY $\left(-\frac{1}{27}\right)^{53}< \left(-\frac{1}{243}\right)^{23}$

Minh Châu · Answer

$\left(\frac{-1}{27}\right)^{53}$=$\left(\frac{-1}{3}\right)^{3X53}$=$\left(\frac{-1}{3}\right)^{159}$

$\left(\frac{-1}{243}\right)^{23}$=$\left(\frac{-1}{3}\right)^{5X23}$=$\left(\frac{-1}{3}\right)^{115}$

=>$\left(\frac{-1}{3}\right)^{159}$>$\left(\frac{-1}{3}\right)^{115}$

=>$\left(\frac{-1}{27}\right)^{53}$>$\left(\frac{-1}{243}\right)^{23}$

Câu trả lời:

$\left(\frac{-1}{27}\right)^{53}$=$\left(\frac{-1}{3}\right)^{3X53}$=$\left(\frac{-1}{3}\right)^{159}$

$\left(\frac{-1}{243}\right)^{23}$=$\left(\frac{-1}{3}\right)^{5X23}$=$\left(\frac{-1}{3}\right)^{115}$

=>$\left(\frac{-1}{3}\right)^{159}$>$\left(\frac{-1}{3}\right)^{115}$

=>$\left(\frac{-1}{27}\right)^{53}$>$\left(\frac{-1}{243}\right)^{23}$