Finding the inverse modulo . $7^{-2}\pmod {11}$ and $7^{-3}\pmod {11}$

Question

$7^{-1}\pmod{11}$

the above can be found by

$7x\pmod{11}\equiv 1$ and $x=8$

now i am confused on how to find $7^{-2}\pmod{11}$ and $7^{-3}\pmod{11}$ .

Answer 1

Hint $\,\ 7^{-2} \equiv (7^{-1})^2\ $ since $\ 7x\equiv 1\,\Rightarrow\, 7^2 x^2\equiv 1.\,$