Age 15 GCSE Maths question

Please explain how you got the answer, thank you!

7^5*7^6=7^3*7^k Find the value of K

Thanks so much for helping me out

Since everything has a base of seven, just add the exponents where two powers of seven are multiplied by each other. 7^6 * 7^5 = 7^11. Then divide this by 7^3. So subtract 3 from 11. The result is 7^8 = 7^k. Therefore k=8.

16807x117649=343x7^k
1977326743=343x7^k
5764801=7^k
log 5764801=log7^k
log 5764801=k(log7) rule of logarithms
log 5764801 / log 7 = k
6.76078432 / 0.84509804 = k

k=8

7^(5+6) = 7^(3+k)
7^(11) = 7^(3+k)
11 = 3 + k
k = 11 - 3 = 8

7^5*7^6=7^3*7^k
7^11=7^(3+k)
11=3+k
k=8

I think it 3