a, Ta có :
\(\left|-2\right|^{300}=2^{300}\)\(\left(1\right)\)
\(\left|-4\right|^{150}=4^{150}=\left(2^2\right)^{150}=2^{300}\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\left|-2\right|^{300}=\left|-4\right|^{150}\)
b, Ta có :
\(\left|-2\right|^{300}=2^{300}=\left(2^3\right)^{100}=8^{100}\)\(\left(1\right)\)
\(\left|-3\right|^{200}=3^{200}=\left(3^2\right)^{100}=9^{100}\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\left|-2\right|^{300}< \left|-3\right|^{200}\)
So sánh;
a,\(\left|-2\right|^{300}\) và \(\left|-4\right|^{150}\)
\(\Rightarrow\left|-2\right|^{300}=2^{300}\)
\(\Rightarrow\left|-4\right|^{150}=4^{150}=\left(2^2\right)^{150}=2^{300}\)
Vậy \(\left|-2\right|^{300}=\left|-4\right|^{150}\)
b,\(\left|-2\right|^{300}\) và \(\left|-3\right|^{200}\)
\(\Rightarrow\left|-2\right|^{300}=2^{300}=\left(2^3\right)^{150}=8^{150}\)
\(\Rightarrow\left|-3\right|^{200}=3^{200}=\left(3^2\right)^{100}=9^{100}\)
Vậy \(\left|-2\right|^{300}< \left|-3\right|^{200}\)
