Answer: The correct option is (C) [tex]\dfrac{4^6}{5^6}.[/tex]
Step-by-step explanation: We are given to select the fraction that is equivalent to the following fraction :
[tex]F=\left(\dfrac{4}{5}\right)^6.[/tex]
We will be using the following property of exponents :
[tex]\left(\dfrac{x}{y}\right)^z=\dfrac{x^z}{y^z}.[/tex]
Therefore, for the given fraction, we have
[tex]F=\left(\dfrac{4}{5}\right)^6=\dfrac{4^6}{5^6}.[/tex]
Thus, the correct option is (C).
