If $${\left( {\sqrt 5 } \right)^7} \div {\left( {\sqrt 5 } \right)^5} = {{\text{5}}^{\text{P}}}{\text{,}}$$     then the value of P is?

Solution (By Examveda Team)

$$\eqalign{ & {\left( {\sqrt 5 } \right)^7} \div {\left( {\sqrt 5 } \right)^5}{\text{ = }}{{\text{5}}^{\text{P}}} \cr & \Rightarrow \frac{{{{\left( {\sqrt 5 } \right)}^7}}}{{{{\left( {\sqrt 5 } \right)}^5}}} = {{\text{5}}^{\text{P}}} \cr & \Rightarrow {\left( {\sqrt 5 } \right)^2} = {{\text{5}}^{\text{P}}} \cr & \Rightarrow {{\text{5}}^{\text{1}}} = {\text{ }}{{\text{5}}^{\text{P}}} \cr & \Rightarrow \boxed{{\text{P}} = 1} \cr} $$