The expression that is correctly developed to use the Power Rule of Exponents is:
\((7^8) \cdot (7^{10})\)
This expression can be simplified using the Power Rule of Exponents which states that when you multiply like bases, you add the exponents:
\[ 7^8 \cdot 7^{10} = 7^{8+10} = 7^{18} \]
The other options do not represent a correct application of the Power Rule for exponents:
- \((7^4)^8\) would involve the Power of a Power rule, which states that \((a^m)^n = a^{m \cdot n}\) but is not relevant here.
- \(12^9\) is just a single number raised to a power and doesn't involve the Power Rule of Exponents.
- \((-5)^0\) equals 1 due to the zero exponent rule, but also doesn't apply the Power Rule directly in a way that involves combining exponents.
Therefore, the first response is the most suitable for the Power Rule of Exponents.