Question

so sánh 2 số: (\(\dfrac{1}{5}\))\(^{45}\) và (\(\dfrac{-1}{2}\))\(^{60}\)

Answer 1

\(\left(\dfrac{1}{5}\right)^{45}\) = \(\dfrac{1^{45}}{5^{45}}\) =\(\dfrac{1}{5^{45}}\)<\(\dfrac{1}{5^{44}}\)= \(\dfrac{1}{\left(5^2\right)^{22}}\) =\(\dfrac{1}{25^{22}}\)

\(\left(\dfrac{-1}{2}\right)^{60}\) = \(\dfrac{\left(-1\right)^{60}}{2^{60}}\)= \(\dfrac{1}{\left(2^4\right)^{15}}\) = \(\dfrac{1}{16^{15}}\)

Vì 25²² > 16¹⁵ =>​ \(\dfrac{1}{25^{22}}\) <\(\dfrac{1}{16^{15}}\)

=>\(\left(\dfrac{1}{5}\right)^{45}< \left(\dfrac{-1}{2}\right)^{60}\)