Question

So sánh 

a/ /-2/³⁰⁰ và /-4/¹⁵⁰

 

b/ /-2/³⁰⁰ và /-3/200

Answer 1

a)\(\left|-2\right|^{300}=2^{300}=\left(2^2\right)^{150}=4^{150}\) ; \(\left|-4\right|^{150}=4^{150}\)

\(\Rightarrow\left|-2\right|^{300}=\left| -4\right|^{150}\)

b) \(\left|-2\right|^{300}=2^{300}=\left(2^3\right)^{100}=8^{100}\) ; \(\left|-3\right|^{200}=3^{200}=\left(3^2\right)^{100}=9^{100}\)

Mà 8 < 9 \(\Rightarrow8^{100}< 9^{100}\) hay \(\left|-2\right|^{300}< \left|-3\right|^{200}\)