If there are $5$  geometric means between $\frac{1}{4}$  and $1024$ , then $r=$

$5$  geometric means between $\frac{1}{4},1024$

$\frac{1}{4},x_1,x_2,x_3,x_4,x_5,1024$

$a=\frac{1}{4},a_7=1024$

$a{r}^6=1024$

$\frac{1}{4}{r}^6=1024$

$r^6=1024\times 4$

$r^6=4096=2^{12}$

$r^6={\left(2^2\right)}^6$

$r^6=4^6$

$r=4$