Simplify Powers of 10: 10^5 × 10^7 × 10^2 Step by Step

To solve this problem, we will apply the product of powers rule, which states that when multiplying powers with the same base, we add the exponents together.

Let's go through each step:

• Identify the expression: $10^5 \times 10^7 \times 10^2$.

• Notice that the base for all terms is 10, so we apply the product of powers rule: $a^m \times a^n = a^{m+n}$.

• Add the exponents: $5 + 7 + 2$.

Now, calculate the sum of the exponents:

$5 + 7 + 2 = 14$.

Therefore, according to the rule, the expression simplifies to:

$10^{5+7+2}=10^{14}$.