## Smallest integer such its n-th root,decimal root followed by 10 consecutive zeros

Determine the smallest possible positive integer P which is not a perfect n-th power, but in the decimal expansion of its n-th root, the decimal point is followed by at least ten consecutive zeroes.

n = 2

$\sqrt {25000000000000000001} \; = \; 5 000000000. \overline{0000000000}99999...$

n = 3

$\sqrt[3]{ \,192459820704257 \,} \; = \; 57736.\overline{0000000000}9999662923...$

n = 4

$\sqrt[4]{ \,3400940858897 \,} \; = \; 1358.\overline{0000000000}9982531...$

n = 5

$\sqrt[5]{ \,428232184833 \,} \; = \; 212.\overline{0000000000}9901...$

n = 6

$\sqrt[6]{ \,117649000001 \,} \; = \; 70.\overline{0000000000}99165...$

n = 7

$\sqrt[7]{ \,52523350145 \,} \; = \; 34.\overline{0000000000}9247...$

n = 8

$\sqrt[8]{ \,25600000001 \,} \; = \; 20.\overline{0000000000}9765...$

n = 9

$\sqrt[9]{ \,20661046785 \,} \; = \; 14.\overline{0000000000}7528...$