Power Play

Number Theory Level 3

The smallest number $n$ greater than 1 such that $\large \sqrt{n}$ , $\large \sqrt[3]{n}$ , $\large \sqrt[4]{n}$ , $\large \sqrt[5]{n}$ , $\large \sqrt[6]{n}$ , $\large \sqrt[7]{n}$ , $\large \sqrt[8]{n}$ , $\large \sqrt[9]{n}$ , $\large \sqrt[10]{n}$ are all integers can be expressed in the form $a^{b}$ , where $a$ and $b$ are both positive integers and with $a$ as small as possible.

Find $a+b$ .