[ Numerical inequalities. Comparing numbers.]

What is greater

a) $2^{300}$ or $3^{200}$ ?

b) $2^{40}$ or $3^{28} ?$

c) $5^{44}$ or $4^{53}$ ?
a) $3^{2}=9>8=2^{3}$, so $3^{200}>2^{300}$.

b) $2^{10}=1024<2187=3^{7}$, so $2^{40}<3^{28}$.

c) $10^{3}<2^{10}$, so $2^{45} \cdot 5^{45}=10^{45}<2^{150}=2^{44} \cdot 4^{53}$, which means $10 \cdot 5^{44}<4^{53}$.

## Answer

a) $3^{200}$;
b) $3^{28}$;
c) $4^{53}$.