A number theory problem by shivam rajoriya

After the first look of the problem we can see that there is use of some modular arithmetic.Thus, $7^{2}\equiv2\pmod{47}$ $\Longrightarrow7^{12}\equiv2^6\pmod{47}.$ But $2^{6}=64\equiv17\pmod{47}.$

it is asked that what is the remainder so (7)raise to the power12/47so we can write it as (47+2)raise to the power 6/47 so by reaminder theorem when p(x)/x+a the remainder is p(a) here 'a' is 0 so here the remainder is (2 )raise to the power 6which is 64 and the remainder is 64-47=17.

Answer is 17