1. If $a=8^{53}, b=16^{41}$ and $c=64^{27}$, then which of the following inequalities is true?
(A) $a>b>c$
(B) $c>b>a$
(C) $b>a>c$
(D) $b>c>a$
(E) $c>a>b$
1. Answer: (D)
First note that $c=\left(8^{2}\right)^{27}=8^{54}$, so we see that $c>a$. Next, $b=\left(4^{2}\right)^{41}=4^{82}$ and $c=\left(4^{3}\right)^{27}=4^{81}$. Therefore we have $b>c$. Consequently $b>c>a$.