Answer
(a) $p_1^{3e_1}p_2^{3e_2}\cdots p_k^{3e_k}$
(b) $6468, (2772)^3$
Work Step by Step
(a) Given $a=p_1^{e_1}p_2^{e_2}\cdots p_k^{e_k}$, we have
$a^3=p_1^{3e_1}p_2^{3e_2}\cdots p_k^{3e_k}$
(b) To find the least positive integer $k$, let $2^4\cdot 3^5\cdot 7\cdot 11^2\cdot k=2^6\cdot 3^6\cdot 7^3\cdot 11^3$, we have:
$k=2^2\cdot 3\cdot 7^2\cdot 11=6468$ and
$2^4\cdot 3^5\cdot 7^2\cdot 11^2\cdot k=(2^2\cdot 3^2\cdot 7\cdot 11)^3=(2772)^3$
