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If $${\left( {\sqrt 5 } \right)^7} \div {\left( {\sqrt 5 } \right)^5} = {{\text{5}}^{\text{P}}}{\text{,}}$$ then the value of P is?
Answer & Solution
Correct Answer:
Option
D
$$\eqalign{
& {\left( {\sqrt 5 } \right)^7} \div {\left( {\sqrt 5 } \right)^5}{\text{ = }}{{\text{5}}^{\text{P}}} \cr
& \Rightarrow \frac{{{{\left( {\sqrt 5 } \right)}^7}}}{{{{\left( {\sqrt 5 } \right)}^5}}} = {{\text{5}}^{\text{P}}} \cr
& \Rightarrow {\left( {\sqrt 5 } \right)^2} = {{\text{5}}^{\text{P}}} \cr
& \Rightarrow {{\text{5}}^{\text{1}}} = {\text{ }}{{\text{5}}^{\text{P}}} \cr
& \Rightarrow \boxed{{\text{P}} = 1} \cr} $$
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