To simplify the expression \((242)^{5}\) using the Power Rule of Exponents, you can apply the rule which states that \((a^m)^n = a^{m \cdot n}\).
Here, you can rewrite the expression as:
\[ (2^{42})^{5} = 2^{42 \cdot 5} = 2^{210} \]
Now looking at the options provided, none seem to match \(2^{210}\). However, if there was a typo or misunderstanding in the original question regarding the base or exponent, \(24^{10}\) would be equivalent to \(2^{210}\) if \(24\) was meant to be \(2^{4}\) which would give \(2^{4*10}=2^{40}\).
However, based on all thoughts, none of these answers is correct based on the simplification derived from the original expression which should be \(2^{210}\).
If you need further clarification or assistance in understanding the exponents or checking a specific option if there's any possible input typo, please let me know!