Answer: The answer is (a) [tex]r^n=a.[/tex]
Step-by-step explanation: The given equation is
[tex]a^{\frac{1}{n}}=r.[/tex]
We are to select from the given options which is the implication of the above equation.
We will be using the following property of logarithm here:
[tex]\{x^b\}^c=x^{b\times c}.[/tex]
Therefore, we have
[tex]a^\frac{1}{n}=r\\\\\Rightarrow \{a^\frac{1}{n}\}^n=r^n\\\\\Rightarrow a^{\frac{1}{n}\times n}=r^n\\\\\Rightarrow a=r^n.[/tex]
Thus, (a) [tex]r^n=a.[/tex] is the correct option.
