$$Statement\ 1\ =>\ x^4=2401$$
$$4\sqrt{x^4}=\pm4\sqrt{2401}$$
$$From\ the\ fractional\ index\ law\ in\ indices$$
$$a^{\frac{1}{b}}=\left(b\sqrt{a}\right)^1$$
$$x^{\frac{4}{4}}=\pm2401^{\frac{1}{4}}$$
$$x=\pm9$$
$$if\ x\ =\ +7\ then\ +7^4=2401$$
$$if\ x\ =-7\ then\ -7^4=2401$$
The exact value of x is unknown as x can either be a positive or negative integer hence statement 1 is NOT SUFFICIENT
$$Statement\ 2\ =>\ x^5=16807$$
$$5\sqrt{\left(x\right)^5}=\pm5\sqrt{16807}$$
$$x^{\frac{5}{5}}=\pm16807^{\frac{1}{5}}$$
$$x=\pm7$$
$$if\ x\ =+7\ then\ +7^5=16807$$
$$but\ if\ x=-7\ then\ -7^5=-16807$$
$$\sin ce\ it\ is\ only\ +7^5\ that\ yields\ 16807\ then\ x=+7$$
$$statement\ 2\ alone\ is\ SUFFICIENT$$
$$Answer\ =\ B$$
