Question

Let $A=\left\{\right(a,b,c):a,b,c\in N,a^{\left(bc\right)}=64\},$ then the total number of ordered triplets is

Answer 1

$a^{\left(bc\right)}=64$
$64=2^6=4^3=8^2={64}^1$

If $a=2$, then $bc=6$
$b=2,c=3;$
$b=3,c=2;$
$b=1,c=6;$
$b=6,c=1$

If $a=4$, then $bc=3$
$b=1,c=3;$
$b=3,c=1$

If $a=8$, then $bc=2$
$b=1,c=2;$
$b=2,c=1$

If $a=64$, then $bc=1$
$b=1,c=1$

Total number of ordered triplets $=4+2+2+1=9$