a) \(2^m-2^n=256\)
\(\Rightarrow2^m-2^n=512-256\)
\(\Rightarrow2^m-2^n=2^9-2^8\)
\(\Rightarrow m=9;n=8\)
b) \(3^m-3^n-162\)
\(\Rightarrow3^m-3^n=243-81\)
\(\Rightarrow3^m-3^n=3^5-3^4\)
\(\Rightarrow m=5;n=4\)
c) \(5^m-5^n=1875000\)
\(\Rightarrow5^m-5^n=5^{10}-5^9\)
\(\Rightarrow m=10;n=9\)