Answer: The correct option is (C)
![(4^6)/(5^6).](https://img.qammunity.org/2019/formulas/mathematics/middle-school/t4uwf2oxb9s9f1wbbabtjo1jodvmr5izcn.png)
Step-by-step explanation: We are given to select the fraction that is equivalent to the following fraction :
![F=\left((4)/(5)\right)^6.](https://img.qammunity.org/2019/formulas/mathematics/middle-school/ccs4b4hzgizqsc8qx6clqwz71lq7m8brtn.png)
We will be using the following property of exponents :
![\left((x)/(y)\right)^z=(x^z)/(y^z).](https://img.qammunity.org/2019/formulas/mathematics/middle-school/rcv7dbs4cqympvdjhmwu4fkg5yoreemn4y.png)
Therefore, for the given fraction, we have
![F=\left((4)/(5)\right)^6=(4^6)/(5^6).](https://img.qammunity.org/2019/formulas/mathematics/middle-school/i7d6s1wqnfwy5ixgrfm3dndlnukkx3it2o.png)
Thus, the correct option is (C).