6. Which of the following is neither a square nor a cube?
A $2^{9}$
B $3^{10}$
C $4^{11}$
D $5^{12}$
E $6^{13}$
6. E Using the index law $a^{m n}=\left(a^{m}\right)^{n}$, we see $2^{9}=\left(2^{3}\right)^{3}$, a cube; $3^{10}=\left(3^{5}\right)^{2}$, a square; $4^{11}=\left(2^{2}\right)^{11}=\left(2^{11}\right)^{2}$, a square; and $5^{12}=\left(5^{4}\right)^{3}$, a cube. This leaves $6^{13}$ which is neither a square nor a cube since 6 is neither a square nor a cube, and 13 is not divisible by 2 nor by 3 .