Answer: The correct options are
(C) 
(D) 
Step-by-step explanation: We are to select the correct pairs that shows equivalent expressions.
We will be using the following property of exponents and radicals :
<u>
</u>
<em><u>Option (A) :</u></em>
The given expressions are
![(\sqrt[3]{125})^7~~\textup{and}~~125^\frac{3}{7}.](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B125%7D%29%5E7~~%5Ctextup%7Band%7D~~125%5E%5Cfrac%7B3%7D%7B7%7D.)
We have
![(\sqrt[3]{125})^7=125^\frac{7}{3}\neq 125^\frac{3}{7}.](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B125%7D%29%5E7%3D125%5E%5Cfrac%7B7%7D%7B3%7D%5Cneq%20125%5E%5Cfrac%7B3%7D%7B7%7D.)
So, the expressions are not equivalent and option (A) is incorrect.
<em><u>Option (B) :</u></em>
The given expressions are

We have
![12^\frac{1}{7}=\sqrt[7]{12},\\\\(\sqrt{12})^7=12^\frac{7}{2}.](https://tex.z-dn.net/?f=12%5E%5Cfrac%7B1%7D%7B7%7D%3D%5Csqrt%5B7%5D%7B12%7D%2C%5C%5C%5C%5C%28%5Csqrt%7B12%7D%29%5E7%3D12%5E%5Cfrac%7B7%7D%7B2%7D.)
So,

Therefore, the expressions are not equivalent and option (B) is incorrect.
<em><u>Option (C) :</u></em>
The given expressions are

We have

Therefore, the expressions are equivalent and option (C) is correct.
<em><u>Option (D) :</u></em>
The given expressions are

We have

Therefore, the expressions are equivalent and option (D) is correct.
Thus, (C) and (D) are the correct options.