Question

[Trần Tiến Luận]

so sánh (-1/6)mủ 100 và (-1/2)mủ 500

Answer 1

[Nguyễn Trần Thành Đạt]

So sánh: \(\left(-\dfrac{1}{6}\right)^{100}\) và \(\left(-\dfrac{1}{2}\right)^{500}\)

Ta có: \(\left(-\dfrac{1}{2}\right)^{500}=\left[\left(-\dfrac{1}{2}\right)^5\right]^{100}=\left(-\dfrac{1}{32}\right)^{100}=\left(\dfrac{1}{32}\right)^{100}\)

\(\left(-\dfrac{1}{6}\right)^{100}=\left(\dfrac{1}{6}\right)^{100}\)

Vì: \(\left(\dfrac{1}{32}\right)^{100}< \left(\dfrac{1}{6}\right)^{100}\Rightarrow\left(-\dfrac{1}{6}\right)^{100}>\left(-\dfrac{1}{2}\right)^{500}\)

Answer 2

[Lalisa Manoban]

\(\left(-\dfrac{1}{6}\right)^{100}\)

\(\left(-\dfrac{1}{2}\right)^{500}\)\(=\left(\left(-\dfrac{1}{2}\right)^5\right)^{100}=\left(\dfrac{-1}{2^5}\right)^{100}=\left(-\dfrac{1}{32}\right)^{100}\)

Vì \(-\dfrac{1}{6}< \left(-\dfrac{1}{32}\right)\)

=>\(\left(-\dfrac{1}{6}\right)^{100}< \left(-\dfrac{1}{32}\right)^{100}\)

Vậy \(\left(-\dfrac{1}{6}\right)^{100}< \left(-\dfrac{1}{2}\right)^{500}\)

#H ( ~~~~~~~Study well~~~~~~~~)