Apply index laws: Evaluate (10)^(200) ÷ (10)^(196) and report the exact numerical value.

Introduction / Context:This is a direct application of exponent subtraction for division with the same base. The goal is to demonstrate fluency with a^m / a^n = a^(m−n).

Given Data / Assumptions:

• (10)^(200) ÷ (10)^(196)
• Base is identical (10).

Concept / Approach:Use the law a^m / a^n = a^(m−n). Subtract exponents and then evaluate the resulting power of 10.

Step-by-Step Solution:(10)^(200) ÷ (10)^(196) = 10^(200 − 196) = 10^410^4 = 10000

Verification / Alternative check:Think place value: shifting decimal four places to the right matches multiplying by 10000.

Why Other Options Are Wrong:1000 (10^3), 100 (10^2), or 100000 (10^5) correspond to incorrect exponent differences. 10 is 10^1.

Common Pitfalls:Accidentally adding exponents during division. Remember division subtracts exponents.

Final Answer:10000