Question

Suppose $3^k\times b^2=6^4$ for some positive integers $k,b$. Find all possible values of $k+b$.

Answer 1

$Now{3}^k\times b^2=6^4\to 3^k\times b^2={(2\times 3)}^4\to 3^k\times b^2=2^4{\times 3}^4\to 3^k\times b^2=3^4\times {\left(2^2\right)}^2\to 3^k\times b^2=3^4\times {\left(4\right)}^{2}ComparingLHS\&RHS,wegetk=4\&b=4\therefore k+b=4+4=8$