1. The problem is to simplify the expression $10^2 \times 10^5$. 2. We use the rule of exponents that states when multiplying powers with the same base, we add the exponents: $$a^m \times a^n = a^{m+n}$$ 3. Applying this rule to our problem: $$10^2 \times 10^5 = 10^{2+5}$$ 4. Simplify the exponent sum: $$10^{7}$$ 5. Therefore, the simplified form of $10^2 \times 10^5$ is $10^7$. This means multiplying 10 squared by 10 to the fifth power results in 10 raised to the seventh power.