Question

If p = 10^m, q = 10^n and p^n*q^m = 100 then prove that mn=1

Answer 1

Explanation:

`\displaystyle\\p=10^m;q=10^n;p^n*q^m=100\\\\p^n*q^m=(10^m)^n*(10^n)^m=10^(mn)*10^(nm)=10^(2mn)=100^(mn)=100\\\\\Rightarrow\ mn=1`