The Product Rule of Exponents states that when multiplying two exponents with the same base, you can add their exponents. However, in your expression \(5^{10} \cdot 5^{5}\), the bases are the same (both are 5), so we can apply this rule.
According to the Product Rule:
\[ a^m \cdot a^n = a^{m+n} \]
For your case:
\[ 5^{10} \cdot 5^{5} = 5^{10+5} = 5^{15} \]
So, \(5^{10} \cdot 5^{5}\) simplifies to \(5^{15}\).