Let's solve the given expression step by step:

\[
\left( \frac{10^7}{10^2} \right) + \left( \frac{10^3}{10^{-2}} \right) \div 10^5
\]

### Step 1: Simplify the first term \(\frac{10^7}{10^2}\)
Using the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\):

\[
\frac{10^7}{10^2} = 10^{7-2} = 10^5
\]

### Step 2: Simplify the second term \(\frac{10^3}{10^{-2}}\)
Again, using the property of exponents:

\[
\frac{10^3}{10^{-2}} = 10^{3 - (-2)} = 10^{3+2} = 10^5
\]

### Step 3: Simplify the entire expression
Now substitute these simplified terms into the original expression:

\[
10^5 + \left( \frac{10^5}{10^5} \right)
\]

\(\frac{10^5}{10^5} = 1\), so the expression becomes:

\[
10^5 + 1 = 100000 + 1 = 100001
\]

Thus, the value of the expression is:

\[
\boxed{100001}
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do we apply the exponent rule to expressions involving division?
2. What happens when we divide powers of 10 with different exponents?
3. How do negative exponents affect the result in division?
4. Can you simplify other expressions using exponent rules like \((\frac{10^n}{10^m})\)?
5. How would this change if we multiplied powers of 10 instead?

**Tip:** Remember, when dividing powers with the same base, you subtract the exponents!

Step-by-step solution for simplifying the expression (10^7 ÷ 10^2) + (10^3 ÷ 10^-2) ÷ 10^5 using exponent rules. Learn how to divide and simplify powers of 10, apply the laws of exponents, and solve this Grade 9-10 math problem with clear explanations.

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